Guido Ubaldus' proof of the existence of God

0 = 0 + 0 + 0 + ...
  = (1 - 1) + (1 - 1) + (1 - 1) + ...
  = 1 - 1 + 1 - 1 + 1 - 1 + ...
  = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ...
  = 1 + 0 + 0 + 0 + ...
  = 1

Ubaldus, a Catholic Saint, felt that this proved the existence of God because "something has been created out of nothing."

It asserts that the series
-1+1-1+1... = sum((-1)^n)
converges to a sum of 0.

Even a high school kid should know that the alternating series diverges.

In my opinion, worse still is that this Ubaldus guy believes that his false proof of 0 = 1 means that god must exist! If anything, it should only prove that 0 = 1 and mathematics = rubbish.

Wait a minute, couldn't one use the exact same reasoning to prove the non-existance of god? A false statement implies anything. It's like asking what would happen if something impossible happened, it is complete rubbish.

1 = 0 = x = 1-1+1-1+1-1+... =

= 1-(1-1+1-1+1-1+...) =

1-x

The point of all this? You cannot parenthesise the elements of an infinite series if it is divergent, and expect results that make sense. You cannot parenthesise the elements of an infinite series that is not absolutely convergent and expect results that make sense (see Riemann's theorem on parenthesising infinite series that converge but not absolutely for even more amazing stuff).

Caution is warranted when doing calculus. Seemingly innocuous expressions may turn out to be meaningless (or to mean something other than what you think they do).

"Very cute. They show us this in calculus as "reasons to be careful with infinite series," but I've never seen it given as a proof of the existence of god... exactly how does it prove the existence of god, anyway? You'd think it'd prove that you can get something from nothing without god."