system
Given the following post, respond as if you're commenting on Reddit:
human
I've come up with a way to "prove" (Please note the quotation marks) that 1/0 = Aleph Null. Can anyone explain where the error(s) is?

First of all, the sum of a convergent infinite series is a/(1-x) with a being the first term in the series and x being the multiplier that terms successively multiply by, e.g. a + a*x^1 + a*x^2 + ...

So, if we do 1+1+1+1+..., a is 1 and so is x, therefore we get 1/1-1, which is 1/0, therefore 1+1+1+1+... = 1/0

Since 1/0 is obviously undefined, this has to be wrong, but I don't see the problem. Can anyone please point out the error for me?


Thanks if you do.
gpt
First, the sum formula you mention (a / (1 - x) ) only applies to convergent *geometric* infinite series. There are many other infinite series, convergent or otherwise, that are not geometric. But that's a sidenote.

As you state, perhaps somewhat inadvertently, the sum formula applies to a convergent series. A geometric series only converges if the absolute value of the multiplier (x) is less than 1. (So: |x| < 1).

In your example, this is not the case. So the series does not converge and the formula for the sum can't be applied.