Talk:Proof of the inconsistency of arithmetic
Who believes this proof? The article has "The proof of the inconsistency of arithmetic is a pseudomathematical proof used by some creationists ..." No evidence is cited of this claim ("used by some creationists"). It appears that there may have been some musing by theists, around 1700, about theological implications of the problems with infinite series, but is any "creationist" (which is a contemporary, political term) actually using this argument? What Grandi wrote over 300 years ago is not terribly relevant now.
The article would be more useful if there are links to actual creationist claims, should such exist. The page cited (How God created the world using the inconsistency of arithmetic is not approving of the claim in the title. It is making a very different point.
The Wikipedia article has much history on Grandi's series. Grandi was criticized, apparently, in an extensive debate with a contemporary, which Grandi won. Proof? The critic died in 1714, Grandi lived to 1742, another 28 years. Ha! Ha! You stupid! You died! Although, as a priest, one might hope that Grandi was not so snarky. --Some random Smith (talk) 21:44, 23 December 2017 (UTC)
Problem with the Proof[edit]
The main problem with the proof is that a series with positive and negative terms can not be rearranged, preserving the sum, unless the series is absolutely convergent. The result 1=0 is itself an indirect proof that the terms cannot be manipulated in the fashion given. Modern analysis requires convergent series of real numbers, ΣAn , to be Cauchy. That is, the sequence {Sn} of partial sums is a convergent sequence, where Sn = A1 + A2 + A3 +.....+An. In this case Sn = 1 or 0 depending upon whether n is odd or even, and is not convergent.Ariel31459 (talk) 02:51, 24 December 2017 (UTC)