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Talk:Essay:pi contains pi (view source)
Revision as of 21:59, September 18, 2022
, 21:59, September 18, 2022Proof by Induction issues
:::Been thinking about this one a lot - where the essay states, "the periodicity may not occur until after an infinite string of digits" - can "endless" be substituted for "infinite?" ICR in its "The God of Infinities" essay states, "Something is infinite if it goes on forever, having no end." so this would seem like a logical substitution. However, "the periodicity may not occur until after an endless stream of digits" is contradictory. ([[User talk:AlChesapeake|talk]]) 10:48, September 18, 2021.
:::Been thinking about this one a lot - where the essay states, "the periodicity may not occur until after an infinite string of digits" - can "endless" be substituted for "infinite?" ICR in its "The God of Infinities" essay states, "Something is infinite if it goes on forever, having no end." so this would seem like a logical substitution. However, "the periodicity may not occur until after an endless stream of digits" is contradictory. ([[User talk:AlChesapeake|talk]]) 10:48, September 18, 2021.
:::Just read Charles Pinter's "A Book of Abstract Algebra" - it has an appendix on inductive proofs and was reminded of this. The Pinter book's text is similar to the article already in Conservapedia [[Proof by Induction]]. The set under discussion must contain first "zero" and it also must contain all n+1 for any n in the set. Using the set of natural numbers, even if something is true for any natural number, that statement is not been proven for infinity, as infinity is not a natural number. It's confusing because infinity is often used as a real number (the integral of 1/x^2 from 1 to infinity results in the natural number one, for example). But in this case, any natural number however large is not the same as infinity. ([[User talk:AlChesapeake|talk]]) 10:48, September 18, 2022.