Difference between revisions of "Essay:pi contains pi"
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: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]]. | :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. | + | Stated another way, no one disputes that pi includes every number that has a finite representation. Thus pi includes itself in all of its increasingly precise representations, without limit, and therefore pi contains pi itself within a vanishingly small margin of error. |
== Strings without termination == | == Strings without termination == | ||
Revision as of 03:07, August 5, 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, no one disputes that pi includes every number that has a finite representation. Thus pi includes itself in all of its increasingly precise representations, without limit, and therefore pi contains pi itself within a vanishingly small margin of error.
Strings without termination
Pi has no termination in its digital representation, no patterns in the digits, and no repetitive periodicity. Pi containing pi can be viewed as two strings: the original pi without termination in its digital representation, and another pi that starts within pi but also without any termination point.
Analogy to Life and Eternity
Stumbling into the "pi within pi" amid another otherwise random string of numbers can seem eerily similar to happening upon eternity in heaven or hell. While the math question has a math answer, the implications for the existence of eternity are unmistakable.