Difference between revisions of "Essay:pi contains pi"
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Stated another way, pi includes every number that has a finite representation. Thus pi includes itself in all of its increasingly precise representations, without limit, and therefore contains pi within a vanishingly small margin of error. | Stated another way, pi includes every number that has a finite representation. Thus pi includes itself in all of its increasingly precise representations, without limit, and therefore contains pi within a vanishingly small margin of error. | ||
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| + | == See also == | ||
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| + | *[https://www.reddit.com/r/explainlikeimfive/comments/1zm55o/eli5_does_pi_contain_itself/ Reddit commentary] | ||
[[category:Essays]] | [[category:Essays]] | ||
[[category:mathematics]] | [[category:mathematics]] | ||
Revision as of 22:45, August 4, 2021
Pi contains pi as showing by proof by induction:
- 1. pi contains pi as one significant digit in a finite representation ("3": 3.141592653....)
- 2. assume pi contains pi as n significant digits in a finite representation of pi. Pi must also contain pi as n+1 significant digits as the number of digits of pi is stretched to infinity.
Stated another way, pi includes every number that has a finite representation. Thus pi includes itself in all of its increasingly precise representations, without limit, and therefore contains pi within a vanishingly small margin of error.