https://conservapedia.com/api.php?action=feedcontributions&user=EdBot&feedformat=atomConservapedia - User contributions [en]2021-01-21T22:09:44ZUser contributionsMediaWiki 1.24.2https://conservapedia.com/index.php?title=%22Must_pass%22_Bill&diff=810734"Must pass" Bill2010-08-22T04:42:36Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>A '''"must pass" bill''' is a vitally important measure that [[Congress]] must enact, such as annual money [[bill|bills]] to fund operations of the [[government]]. Because of their must-pass quality, these measures often attract "[[riders]]" (unrelated [[policy]] [[provisos]]).<ref>[http://www.senate.gov/reference/glossary_term/appropriation.htm] US Senate Reference</ref><br />
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[[Category:United States Government Word Definitions]]</div>EdBothttps://conservapedia.com/index.php?title=Adjourn_for_more_than_three_days&diff=810733Adjourn for more than three days2010-08-22T04:42:22Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>Under the [[United States Constitution|Constitution]], neither chamber may [[adjourn]] for more than three days without the approval of the other. Such approval is obtained in a [[concurrent resolution]] approved by both chambers.<ref>[http://www.senate.gov/reference/glossary_term/adjourn_more_than_3_days.htm] US Senate Reference</ref><br />
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[[Category:United States Government Word Definitions]]<br />
[[Category:United States Senate Terms]]</div>EdBothttps://conservapedia.com/index.php?title=Hickory-Smoked_Ham&diff=810732Hickory-Smoked Ham2010-08-22T04:42:21Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>A '''hickory-smoked ham''' is a cured [[ham]] which has been smoked by hanging over burning hickory wood chips in a smokehouse. The ham may not be labeled “hickory smoked” unless hickory wood has been used.<br />
==References==<br />
[http://www.fsis.usda.gov/Help/A-Z_Index/index.asp USDA Index]<br />
[[Category:United States Government Word Definitions]]</div>EdBothttps://conservapedia.com/index.php?title=Act&diff=810731Act2010-08-22T04:42:06Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>An '''act''' is legislation (a [[bill]] or [[joint resolution]]) which has passed both chambers of [[Congress]] in identical form, been signed into law by the [[President of the United States of America|President]], or passed over his [[veto]], thus becoming a law. Technically, this term also refers to a [[bill]] that as been passed by one house and engrossed (prepared as an official copy).<ref>[http://www.senate.gov/reference/glossary_term/act.htm US Senate Reference]</ref><br />
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[[Category:United States Government Word Definitions]]<br />
[[Category:United States Senate Terms]]</div>EdBothttps://conservapedia.com/index.php?title=Headcheese&diff=810730Headcheese2010-08-22T04:42:05Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>A jellied [[product]] consisting predominantly of pork by[[product]]s and seasoning ingredients. It must contain some [[product]] from the head.<br />
==References==<br />
[http://www.fsis.usda.gov/Help/A-Z_Index/index.asp USDA Index]<br />
[[Category:United States Government Word Definitions]]</div>EdBothttps://conservapedia.com/index.php?title=Habitat_composition&diff=810729Habitat composition2010-08-22T04:42:03Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>'''Habitat composition''' is - according to the [[USDA]] terminology - ''"the makeup or relative proportion of the [[general cover]] categories occurring about a point."<ref>[http://www.nrcs.usda.gov/technical/NRI/1997/summary_report/glossary.html List of USDA terminology]</ref>''<br />
==References== <br />
<references /><br />
[[Category:Agriculture]]<br />
{{USDA_Terms}}</div>EdBothttps://conservapedia.com/index.php?title=Hayland&diff=810728Hayland2010-08-22T04:42:02Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>'''Hayland''' is - according to the [[USDA]] terminology - ''"a subcategory of [[cropland]] managed for the production of forage crops that are machine harvested. The crop may be grasses, legumes, or a combination of both. Hayland also includes land in set-aside or other short-term agricultural programs."<ref>[http://www.nrcs.usda.gov/technical/NRI/1997/summary_report/glossary.html List of USDA terminology]</ref>''<br />
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[[Category:Agriculture]]<br />
{{USDA_Terms}}</div>EdBothttps://conservapedia.com/index.php?title=Adjourn&diff=810727Adjourn2010-08-22T04:42:01Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>A motion to '''adjourn''' in the [[Senate]] (or a [[committee]]) ends that day's session.<ref>[http://www.senate.gov/reference/glossary_term/adjourn.htm] US Senate Reference</ref><br />
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==See also==<br />
*[[Adjourn for more than three days]]<br />
*[[Adjournment Sine Die]]<br />
[[Category:United States Government Word Definitions]]<br />
[[Category:United States Senate Terms]]</div>EdBothttps://conservapedia.com/index.php?title=Honey-Cured&diff=810726Honey-Cured2010-08-22T04:42:00Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>'''Honey-cured''' may be shown on the labeling of a [[cured]] [[product]] if [[honey]] is the only sweetening ingredient or is at least half the sweetening ingredients used, and if the honey is used in an amount sufficient to [[flavor]] and/or affect the appearance of the finished [[product]].<br />
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Common foodstuffs that are honey-cured include ham, bacon, and turkey.<br />
==References==<br />
*[http://www.fsis.usda.gov/Help/A-Z_Index/index.asp USDA Index]<br />
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[[Category:United States Government Word Definitions]]</div>EdBothttps://conservapedia.com/index.php?title=Growing_season&diff=810725Growing season2010-08-22T04:42:00Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Jpatt</p>
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<div>'''Growing season''' is - according to the [[USDA]] terminology - ''" the '''frost-free season''', the period and/or number of days between the last freeze in the [[spring]] and the first frost in the fall for the freeze threshold temperature of the crop or other designated temperature threshold."<ref>[http://www.nrcs.usda.gov/technical/NRI/1997/summary_report/glossary.html List of USDA terminology]</ref>''<br />
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It varies according to the location, and more specifically according to the altitude, latitude, and proximity to large bodies of water.<br />
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Contrary to popular misconception, the "growing season" is not the only time when crops grow. Many crops, including winter wheat, oats, rye, canola/rutabaga, and kale, are grown partly or wholly during times of year other than the frost-free season.<br />
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[[Category:Agriculture]]<br />
{{USDA_Terms}}</div>EdBothttps://conservapedia.com/index.php?title=Advice_and_consent&diff=810723Advice and consent2010-08-22T04:41:57Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>Under the [[United States Constitution|Constitution]], [[president]]ial nominations for executive and judicial posts take effect only when confirmed by the [[Senate]], and international treaties become effective only when the Senate approves them by a two-thirds vote.<ref>[http://www.senate.gov/reference/glossary_term/advice_and_consent.htm] US Senate Reference</ref><br />
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==References==<br />
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[[Category:United States Government Word Definitions]]<br />
[[Category:United States Senate Terms]]</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_I&diff=810724American Government Terms I2010-08-22T04:41:57Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}<br />
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[[Implied Powers]]<br />
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[[Incorporation Doctrine]]<br />
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[[Interest Group]]<br />
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[[Intergovernmental Lobbying]]<br />
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[[Interstate Compact]]<br />
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[[Interstate Rendition Clause]]<br />
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[[Investigation]]<br />
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[[Issue Network]]<br />
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<div>{{American Government Terms}}<br />
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[[Hard Money]]<br />
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[[Hate Speech]]<br />
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<div>{{American Government Terms}}<br />
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*[[National Committee]]<br />
*[[National Security Council]]<br />
*[[National Voter Registration Act]]<br />
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*[[Necessary and Proper Clause]]<br />
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*[[North American Free Trade Agreement (NAFTA)]]</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_C&diff=810720American Government Terms C2010-08-22T04:41:38Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}<br />
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[[Capital-gains Clause]]<br />
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[[Capital-gains Tax]]<br />
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[[Casework]]<br />
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[[Categorical Grant]]<br />
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[[Caucus]]<br />
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[[Centralized Federalism]]<br />
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[[Chairman]]<br />
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[[Chaplain]]<br />
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[[Checks and Balances]]<br />
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[[Christmas Tree (Government)]]<br />
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[[Class]]<br />
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[[Clean Bill]]<br />
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[[Clear and Present Danger Test]]<br />
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[[Cloakroom]]<br />
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[[Closed Convention]]<br />
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[[Closed Primary]]<br />
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[[Closed Rule]]<br />
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[[Cloture]]<br />
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[[Coattail effect]]<br />
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[[Cofederal System]]<br />
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[[Commerce Clause]]<br />
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[[Committee]]<br />
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[[Committee Amendment]]<br />
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[[Committee Calendar]]<br />
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[[Committee Jurisdiction]]<br />
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[[Committee Membership]]<br />
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[[Committee on Committees]]<br />
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[[Committee Print]]<br />
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[[Committee Substitute]]<br />
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[[Committee of the Whole]]<br />
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[[Committee Report]]<br />
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[[Compact Clause]]<br />
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[[Companion Bill or Measure]]<br />
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[[Comparable Worth]]<br />
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[[Compromise Bill]]<br />
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[[Compulsory Process Clause]]<br />
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[[Concurrent Powers]]<br />
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[[Concurring Opinion]]<br />
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[[Concurrent Resolution]]<br />
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[[Conditional Adjournment]]<br />
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[[Conditions of Aid]]<br />
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[[Conferees]]<br />
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[[Conference Committee]]<br />
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[[Conference, party]]<br />
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[[Conference Report]]<br />
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[[Confirmation]]<br />
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[[Confrontation Clause]]<br />
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[[Congressional Budget Office]]<br />
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[[Congressional Research Service]]<br />
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[[Congressional Record]]<br />
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[[Congressional Review]]<br />
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[[Congressional-executive Agreement]]<br />
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[[Consideration]]<br />
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[[Continuing Resolution/Continuing Appropriations]]<br />
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[[Constitution]]<br />
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[[Constitutional Convention]]<br />
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[[Constitutional Courts]]<br />
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[[Controlled Time]]<br />
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[[Cooperative Federalism]]<br />
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[[Copyright Clause]]<br />
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[[Cost-benefit Analysis]]<br />
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[[Council of Economic Advisers]]<br />
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[[Creative Federalism]]<br />
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[[Cross-ownership]]<br />
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[[Cruel and Unusual Punishments Clause]]</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_K&diff=810719American Government Terms K2010-08-22T04:41:36Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}<br />
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[[Keynesian Economics]]</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_J&diff=810718American Government Terms J2010-08-22T04:41:34Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}<br />
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[[Jim Crow Laws]]<br />
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[[Joint Committee]]<br />
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[[Joint Meeting]]<br />
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[[Joint Session]]<br />
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<div>{{American Government Terms}}<br />
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[[Abington School District v. Schempp]]<br />
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[[Absentee ballot]]<br />
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[[Act]]<br />
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[[Adjourn]]<br />
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[[Adjourn for more than three days]]<br />
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[[Adjournment Sine Die]]<br />
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[[Adjournment to a Day and Time Certain]]<br />
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[[Administrative Agencies]]<br />
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[[Agenda Setting]]<br />
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[[Amendment]]<br />
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[[Amendment in the Nature of a Substitute]]<br />
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[[Amicus curiae brief]]<br />
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[[Anti-Federalists]]<br />
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[[Appeal]]<br />
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[[Appellate jurisdiction]]<br />
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[[Appointments Clause]]<br />
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[[Appropriation]]<br />
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[[Appropriations Clause]]<br />
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[[Army Clause]]<br />
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[[Articles of Confederation]]<br />
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[[Attorney General]]<br />
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[[Authorization]]<br />
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[[Authorizations Act]]</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_M&diff=810716American Government Terms M2010-08-22T04:41:32Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}<br />
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*[[Majority Leader]]<br />
*[[Majority Whip]]<br />
*[[Mandate]]<br />
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*[[Marble Cake Federalism]]<br />
*[[Margin of Error]]<br />
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*[[McGovern-Fraser Commission]]<br />
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*[[Measure]]<br />
*[[Media event]]<br />
*[[Midterm elections]]<br />
*[[Minimum-rationality standard]]<br />
*[[Minority Leader]]<br />
*[[Minority Whip]]<br />
*[[Miranda warning]]<br />
*[[Modified Closed Rule]]<br />
*[[Modified Open Rule]]<br />
*[[Monetary policy]]<br />
*[[Morning Business]]<br />
*[[Motion to Proceed to Consider]]<br />
*[[Motor Voter Act]]<br />
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*[["Must pass" Bill]]</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_L&diff=810715American Government Terms L2010-08-22T04:41:31Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}<br />
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*[[Laissez-faire Economics]]<br />
*[["Lame duck" Session]]<br />
*[[LAPS Test]]<br />
*[[Layer cake federalism]]<br />
*[[Layover]]<br />
*[[Leak]]<br />
*[[Leave to Sit]]<br />
*[[Legislative]]<br />
*[[Legislative Branch]]<br />
*[[Legislative Courts]]<br />
*[[Legislative Day]]<br />
*[[Legislative Session]]<br />
*[[Legislative Veto]]<br />
*[[Lemon Test]]<br />
*[[Line-item veto]]<br />
*[[Line-item Veto Act]]<br />
*[[Lobbying]]<br />
*[[Logrolling]]</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_Q&diff=810714American Government Terms Q2010-08-22T04:41:03Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}<br />
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*[[Question]]<br />
*[[Quorum]]<br />
*[[Quorum Call]]</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_O&diff=810713American Government Terms O2010-08-22T04:41:02Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}<br />
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*[[Obligation]]<br />
*[[Off-budget Entities]]<br />
*[[Off the record]]<br />
*[[Office of Management and Budget]]<br />
*[[On backround]]<br />
*[[On deep backround]]<br />
*[[On the record]]<br />
*[[On backround]]<br />
*[[Open convention]]<br />
*[[Open Rule]]<br />
*[[Opinion Clause]]<br />
*[[Original Bill]]<br />
*[[Original jurisdiction]]<br />
*[[Outlays]]<br />
*[[Override of a Veto]]<br />
*[[Oversight]]</div>EdBothttps://conservapedia.com/index.php?title=Amendment_in_the_nature_of_a_substitute&diff=810712Amendment in the nature of a substitute2010-08-22T04:40:58Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>An '''[[amendment]] in the nature of a substitute''' is an amendment that would strike out the entire text of a [[bill]] or other [[measure]] and insert a different full text.<ref>[http://www.senate.gov/reference/glossary_term/amendment_substitute.htm] US Senate Reference</ref><br />
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==References==<br />
<references/><br />
[[Category:United States Government Word Definitions]]<br />
[[Category:United States Senate Terms]]</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms&diff=810711American Government Terms2010-08-22T04:40:57Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{Terms index|American Government|cat= United States Government Word Definitions}}<br />
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''Within each letter, brightly colored (red) links need new descriptions, and the others (blue) need improvement.''<br />
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Using the index, please add more terms relating to the [[United States Government]]!</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_V&diff=810710American Government Terms V2010-08-22T04:40:56Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}<br />
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*[[Value-added tax]]<br />
*[[Veto]]<br />
*[[Vice President of the United States of America|Vice President]]<br />
*[[Virginia Plan]]<br />
*[[Voice Vote]]<br />
*[[Vote]]<br />
*[[Voter apathy]]<br />
*[[Voter turnout]]</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_X&diff=810709American Government Terms X2010-08-22T04:40:56Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_D&diff=810708American Government Terms D2010-08-22T04:40:55Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}<br />
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[[De Facto Segregation]]<br />
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[[Deficit (Surplus)]]<br />
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[[De Jure Segregation]]<br />
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[[Delegate]]<br />
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[[Delegated Powers]]<br />
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[[Deregulation]]<br />
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[[Detente]]<br />
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[[Discount Rate]]<br />
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[[Discretionary Spending]]<br />
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[[Dissenting opinion]]<br />
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[[Divided Government]]<br />
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[[Domino Theory]]<br />
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[[Double Jeopardy]]<br />
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[[Dual federalism]]<br />
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[[Due Federalism]]<br />
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[[Due process]]</div>EdBothttps://conservapedia.com/index.php?title=Appeal&diff=810701Appeal2010-08-22T04:31:05Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>An '''appeal''' is a proceeding brought to a higher court to review a lower court decision. [[Category:Legal Terms]]<br />
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In the [[United States Senate]], when the [[Chair]] rules on a [[point of order]], any [[Senator]] may appeal the ruling, in which case the full Senate makes a final decision on the point of order by voting whether to sustain or reverse the ruling.<ref>[http://www.senate.gov/reference/glossary_term/appeal.htm] US Senate Reference</ref><br />
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==References==<br />
<references/><br />
[[Category:United States Government Word Definitions]]<br />
[[Category:United States Senate Terms]]</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_W&diff=810700American Government Terms W2010-08-22T04:29:55Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}<br />
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*[[War Powers Act]]<br />
*[[Warantless searches]]<br />
*[[Whips]]<br />
*[[White primary]]<br />
*[[Winner-take-all primary]]<br />
*[[Workfare]]<br />
*[[Writ of certiorari]]<br />
*[[Writ of habeas corpus]]</div>EdBothttps://conservapedia.com/index.php?title=American_Government_Terms_T&diff=810699American Government Terms T2010-08-22T04:29:32Z<p>EdBot: Reverted edits by HarryY (Talk) to last revision by Aschlafly</p>
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<div>{{American Government Terms}}<br />
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*[[Table (Government)]]<br />
*[[Take Care Clause]]<br />
*[[Teller Vote]]<br />
*[[Term Limit]]<br />
*[[Three-Fifths Compromise]]<br />
*[[Tinker v. Des Moines Independent Community School Dist.]]<br />
*[[Treaty Clause]]<br />
*[[Trial balloon]]<br />
*[[Trustee]]</div>EdBothttps://conservapedia.com/index.php?title=Category:Nobel_Prize_Laureates&diff=810698Category:Nobel Prize Laureates2010-08-22T04:28:44Z<p>EdBot: Reverted edits by EdBot (Talk) to last revision by WesleyS</p>
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<div>'''The [[Nobel Prize]]s''' are awarded in the following categories:<br />
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[[Category:Nobel Prize]]</div>EdBothttps://conservapedia.com/index.php?title=Category:Nobel_Prize_Laureates&diff=810696Category:Nobel Prize Laureates2010-08-22T04:27:39Z<p>EdBot: Robot: Capitalize category</p>
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<div>'''The [[Nobel Prize]]s''' are awarded in the following categories:<br />
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[[Category:Nobel Prize]] [[Category:Nobel Laureates in Chemistry]]</div>EdBothttps://conservapedia.com/index.php?title=Category:Nobel_Prize_Laureates&diff=810684Category:Nobel Prize Laureates2010-08-22T04:25:01Z<p>EdBot: Reverted edits by EdBot (Talk) to last revision by WesleyS</p>
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<div>'''The [[Nobel Prize]]s''' are awarded in the following categories:<br />
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[[Category:Nobel Prize]]</div>EdBothttps://conservapedia.com/index.php?title=Category:Nobel_Prize_Laureates&diff=810682Category:Nobel Prize Laureates2010-08-22T04:24:27Z<p>EdBot: Robot: Capitalize category</p>
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<div>'''The [[Nobel Prize]]s''' are awarded in the following categories:<br />
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[[Category:Nobel Prize]] [[Category:Nobel Laureates in Chemistry]]</div>EdBothttps://conservapedia.com/index.php?title=Category:Heads_of_State&diff=810631Category:Heads of State2010-08-22T04:19:41Z<p>EdBot: Reverted edits by EdBot (Talk) to last revision by WesleyS</p>
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<div>[[Category:Statesmen]]</div>EdBothttps://conservapedia.com/index.php?title=Category:Heads_of_State&diff=810630Category:Heads of State2010-08-22T04:17:44Z<p>EdBot: Robot: Capitalize category</p>
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<div>[[Category:Statesmen]] [[Category:Roman_emperors]]</div>EdBothttps://conservapedia.com/index.php?title=Category:Heads_of_State&diff=810629Category:Heads of State2010-08-22T04:17:00Z<p>EdBot: Reverted edits by EdBot (Talk) to last revision by WesleyS</p>
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<div>[[Category:Statesmen]]</div>EdBothttps://conservapedia.com/index.php?title=Category:Heads_of_State&diff=810627Category:Heads of State2010-08-22T04:15:36Z<p>EdBot: Robot: Capitalize category</p>
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<div>[[Category:Statesmen]] [[Category:Roman_emperors]]</div>EdBothttps://conservapedia.com/index.php?title=K%C3%B6nig%27s_lemma&diff=810626König's lemma2010-08-22T04:03:08Z<p>EdBot: Robot: Capitalize "Set theory" category</p>
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<div>'''König's lemma''' (also spelled '''Koenig's lemma''' to avoid the [[trema]]) is a result in [[Zermelo-Fraenkel]] Set Theory and [[Graph Theory]]. It states that an infinite [[tree]] with finitely many branching degrees must have an infinite branch. Set theorists consider this to be an important transfinite generalization of the [[Pigeonhole Principle]].<br />
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== See also ==<br />
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[[Königsberg Bridges Problem]]<br />
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[[Category:Advanced Mathematics]] [[Category:Set Theory]]</div>EdBothttps://conservapedia.com/index.php?title=Schr%C3%B6der-Bernstein_theorem&diff=810625Schröder-Bernstein theorem2010-08-22T04:02:31Z<p>EdBot: Robot: Capitalize "Set theory" category</p>
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<div>The '''Schröder-Bernstein theorem''' states:<br />
<blockquote><br />
Let '''A''', '''B''' be [[set]]s, if |'''A'''| ≤ |'''B'''| and |'''B'''| ≤ |'''A'''|, then |'''A'''| = |'''B'''|.<br />
</blockquote><br />
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[[Category:Set Theory]]</div>EdBothttps://conservapedia.com/index.php?title=Set_theory&diff=810622Set theory2010-08-22T03:57:58Z<p>EdBot: Robot: Capitalize "Set theory" category</p>
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<div>'''Set theory''' is a branch of [[mathematics]] dealing with collections of objects. <br />
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*The language of set theory is based on a single fundamental relation, called membership. We say that A is a member of B (in symbols A ∈ B), or that the set B contains A as its element. The understanding is that a set is determined by its elements; in other words, two sets are deemed equal if they have exactly the same elements. <ref>http://plato.stanford.edu/entries/set-theory/</ref><br />
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==History of set theory==<br />
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It was developed in the late 1800s, primarly by the German mathematician [[Georg Cantor]]. This initial attempt became known as "naive set theory" because mathematicians found flaws in it. It was replaced by "axiomatic set theory" in the early 1900s. The most commonly used such axiomatization is [[Zermelo-Fraenkel]] set theory.<br />
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One paradox in naive set theory was announced by [[Bertrand Russell]] in 1901, and is known as [[Russell's Paradox]].<br />
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Like all sufficiently strong mathematical theories, set theory is incomplete, as shown by [[Kurt Godel]]. However, set theory is the received axiomatization of mathematics today, with subjects like analysis, [[algebra]], topology, and [[geometry]] using set theory and its language for their own foundation.<br />
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==The Empty Set==<br />
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The empty set is the set with no members. Because sets are uniquely defined by membership, the empty set is unique. The empty set is usually denoted by {} or ∅.<br />
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==References==<br />
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<References/><br />
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[[Category:Set Theory]]</div>EdBothttps://conservapedia.com/index.php?title=Well-Ordering_Theorem&diff=810621Well-Ordering Theorem2010-08-22T03:57:42Z<p>EdBot: Robot: Capitalize "Set theory" category</p>
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<div>The '''Well-Ordering Theorem''' was proved by Zermelos in 1904, and it states:<br />
<blockquote><br />
''Every set can be well-ordered''.<br />
</blockquote><br />
This result surprised [[mathematician]]s everywhere. The Well-Ordering Theorem is equivalent of the [[Axiom of Choice]], and no well-ordering relation has ever been explicitly constructed for [[uncountable set]]s. Thus, the mathematicians who reject the Axiom of Choice also reject this theorem.<br />
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[[Category:Set Theory]]</div>EdBothttps://conservapedia.com/index.php?title=Empty_set&diff=810620Empty set2010-08-22T03:56:27Z<p>EdBot: Robot: Capitalize "Set theory" category</p>
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<div>In [[set theory]], the '''empty set''', usually denoted <math>\emptyset</math>, is the set without any members. For example, the "set of all blue-eyed lions," the "set of all mermaids," and the "set of all people born in 1700 who are still alive" are all empty sets.<br />
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The empty set is unique, since any two empty sets have precisely the same members (that is, none) and is a [[subset]] of every other set. <br />
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Its existence is postulated by the [[Axiom of empty set]] in the axioms of [[Zermelo–Fraenkel set theory]]. Though this seems counterintuitive, the empty set is a subset of the empty set, and the empty set is [[disjoint]] with itself. More generally, the union of any set with the empty set is the original set, while the intersection of any set with the empty set is itself the empty set.<br />
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[[Category:Set Theory]]</div>EdBothttps://conservapedia.com/index.php?title=Cartesian_product&diff=810619Cartesian product2010-08-22T03:53:09Z<p>EdBot: Robot: Capitalize "Set theory" category</p>
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<div>The '''Cartesian product''' of two [[set]]s ''A'' and ''B'' is the set (usually denoted by ''A &times; B'') consisting of all ordered pairs ''(a, b)'' where <math>a \in A</math> and <math>b \in B</math>. The Cartesian product is named after [[René Descartes]], who invented this concept.<br />
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A common example of a Cartesian product is the [[coordinate plane]], <math>\mathbb{R}^2</math>. This is all ordered pairs ''(a,b)'' of [[real number]]s ''a'' and ''b''. It is used for [[graph]]ing [[function]]s on the real numbers.<br />
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==See also==<br />
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*[[product]]<br />
*[[dot product]]<br />
*[[cross product]]<br />
*[[infinite product]]<br />
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[[Category:Set Theory]]</div>EdBothttps://conservapedia.com/index.php?title=Continuum_hypothesis&diff=810618Continuum hypothesis2010-08-22T03:52:31Z<p>EdBot: Robot: Capitalize "Set theory" category</p>
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<div>The '''Continuum hypothesis''' is a conjecture by [[Georg Cantor]] which states that there is no set with [[cardinality]] greater than all the [[natural number]]s but less than the cardinality of the [[real number]]s (Continuum). Stated another way, this hypothesis holds that there is no set which as a cardinality between that of the natural numbers and that of the real numbers.<br />
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The ''Generalized'' Continuum hypothesis states that there is no set whose cardinality lies between the cardinality of a given set and the cardinality of the set of all subsets of that given set.<br />
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In standard mathematical nomenclature, the cardinality of a set is denoted by the Hebrew letter <math>\aleph</math>. <br />
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Cantor died without knowing the answer to his conjecture of the Continuum hypothesis. [[Kurt Godel]] and [[Paul Cohen]] have since shown that the Continuum hypothesis is [[undecidable]] in [[Zermelo-Fraenkel]] Set Theory.<br />
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[[Category:Set Theory]]</div>EdBothttps://conservapedia.com/index.php?title=Crisp_sets&diff=810617Crisp sets2010-08-22T03:51:33Z<p>EdBot: Robot: Capitalize "Set theory" category</p>
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<div>'''Crisp [[set]]s''' are traditional sets in [[mathematics]], called "crisp" in [[fuzzy logic]] to distinguish crisp sets from fuzzy sets. In crisp sets, an object must either belong to a set or not belong to it.<br />
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[[Category:Set Theory]]</div>EdBothttps://conservapedia.com/index.php?title=Russell%27s_Paradox&diff=810615Russell's Paradox2010-08-22T03:50:09Z<p>EdBot: Robot: Capitalize "Set theory" category</p>
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<div>[[Bertrand Russell]]'s Paradox revealed a flaw in 1901 in early or naive [[set theory]]. (It is likely others saw this flaw before [[Bertrand Russell]].) It is a form of the [[liar's paradox]] expressed in the terms of [[set theory]].<br />
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The defect is as follows. Let S be the set of all sets that do not contain themselves as members. In other words, set T is an element of S if, and only if, T is not an element of T:<br />
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: <math>S=\{T\mid T\not\in T\}.</math><br />
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Here is the flaw. Is Set S a member of itself? If S is a member of itself, then it cannot be a member of itself by the very definition of S. But if S is not a member of itself, then it must be a member of itself, again by its very definition. Hence there is a fundamental logical contradiction in this type of set, and in any theory that allows it. In formal terms,<br />
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:<math> S\in S \iff S\not\in S.</math><br />
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Russel's paradox and others like it can be avoided only at the expense of giving up the idea that any criteria can be used to construct sets. For example in [[Zermelo-Fraenkel]] set theory the construction <math>S=\{T\mid T\not\in T\}</math> would not qualify as [[well-founded]]. Some formulations of set theory would allow such a construction but then S would be a [[proper class]] rather than a set.<br />
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==External Links==<br />
:[http://plato.stanford.edu/entries/russell-paradox/ Russell's Paradox at Stanford Encyclopedia of Philosophy]<br />
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[[Category:Set Theory]]</div>EdBothttps://conservapedia.com/index.php?title=Symmetric_difference&diff=810614Symmetric difference2010-08-22T03:49:30Z<p>EdBot: Robot: Capitalize "Set theory" category</p>
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<div>The '''symmetric difference''' between two sets A and B (denoted A&Delta;B) is given as:<br />
<math>A\Delta B = (A\backslash B)\cup (B\backslash A)</math>.<br />
This operator is [[symmetry|symmetric]] in that A&Delta;B=B&Delta;A. Also, A&Delta;A is the empty set, while the symmetric difference of the empty set with any set is that set.<br />
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The set-theoretic operator &Delta; obeys several laws:<br />
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<math><br />
A\Delta (C\backslash B) = (A\Delta C)\backslash B<br />
</math><br />
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<math><br />
A\Delta \cup_{i\in I} B_i = \cup_{i\in I} A\Delta B_i<br />
</math><br />
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<math><br />
A\Delta \cap_{i\in I} B_i = \cap_{i\in I} A\Delta B_i<br />
</math><br />
<br />
<math><br />
A\Delta (B\Delta C) = (A\Delta B)\cap (A\Delta C)<br />
</math><br />
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Symmetric differences are used to create [[filters]] for [[forcing]] constructions.<br />
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[[Category:Set Theory]]</div>EdBothttps://conservapedia.com/index.php?title=Symmetric_difference&diff=810612Symmetric difference2010-08-22T03:43:48Z<p>EdBot: Robot: Capitalize "Set theory" category</p>
<hr />
<div>The '''symmetric difference''' between two sets A and B (denoted A&Delta;B) is given as:<br />
<math>A\Delta B = (A\backslash B)\cup (B\backslash A)</math>.<br />
This operator is [[symmetry|symmetric]] in that A&Delta;B=B&Delta;A. Also, A&Delta;A is the empty set, while the symmetric difference of the empty set with any set is that set.<br />
<br />
The set-theoretic operator &Delta; obeys several laws:<br />
<br />
<math><br />
A\Delta (C\backslash B) = (A\Delta C)\backslash B<br />
</math><br />
<br />
<math><br />
A\Delta \cup_{i\in I} B_i = \cup_{i\in I} A\Delta B_i<br />
</math><br />
<br />
<math><br />
A\Delta \cap_{i\in I} B_i = \cap_{i\in I} A\Delta B_i<br />
</math><br />
<br />
<math><br />
A\Delta (B\Delta C) = (A\Delta B)\cap (A\Delta C)<br />
</math><br />
<br />
Symmetric differences are used to create [[filters]] for [[forcing]] constructions.<br />
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[[Category:Set_theory]] [[Category:Set Theory]]</div>EdBothttps://conservapedia.com/index.php?title=Surjection&diff=810610Surjection2010-08-22T03:24:37Z<p>EdBot: Robot: Capitalize "Set theory" category</p>
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<div>{{Math-m}}<br />
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A '''surjection''' or '''surjective function''' is a mapping (or [[function]]) between two [[set]]s, that is "onto". This means that the function "hits" every point in the range. That is, no point in the range isn't mapped to.<br />
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In other words, a surjection from set A to set B is a mapping such that every element in B has some element in A mapped to it. For example, one surjection between the sets {X, Y, Z} and {1, 2}, maps: X to 1, Y to 2, and Z also to 2. If we were use this map instead: X to 1, Y to 1, and Z to 1, it would fail to be "onto" because nothing maps to 2.<br />
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For further information, see [[bijection]]<br />
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[[Category:Mathematics]] [[Category:Set Theory]]</div>EdBot