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Talk:Essay:pi contains pi (view source)
Revision as of 21:05, April 19, 2024
, 21:05, April 19, 2024→MayGodBless's thoughts: new section
:::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.
:::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.
== MayGodBless's thoughts ==
I agree with the [[logic]] in this essay, but not its conclusion. I agree that for all epsilon > 0 there is a representation of pi within pi such that the "error" is no more than epsilon, but this is not the same as pi containing pi.
For an example with similar logic, consider f(x)=x/x. The limit as x tends to 0 of f(x) is 1, but f(0) is undefined. [[User:MayGodBless|MayGodBless]] ([[User talk:MayGodBless|talk]]) 17:05, April 19, 2024 (EDT)