this post was submitted on 22 Jul 2026
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Math Thematic

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Proof that 0 is infinity (lemmy.nz)
submitted 3 weeks ago* (last edited 3 weeks ago) by xiao@sh.itjust.works to c/Math_history@sh.itjust.works
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1 = 1

1 = (-1) + 2

1 = (-2) + 3

1 = (-3) + 4

1 = (-4) + 5 ... And so on...

By adding term by term to all these equations, we get: 1 + 1 + 1 + 1 + 1 + 1 + ... = 1 + (-1) + 2 + (-2) + 3 + (-3) + 4 + (-4) + 5 + ...

In the expression on the right, all the terms cancel out in pairs, giving: 1 + 1 + 1 + 1 + 1 + 1 + ... = 0

The expression on the left, consisting of an infinite sum of terms equal to 1, tends to infinity. Thus, 0 is equal to infinity.

And yet 0 is not equal to infinity. So where is the mistake?

Before to answerIn case that you decide to write it down please hide your answer to let others think about it ๐Ÿ‘

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[โ€“] one_old_coder@piefed.social 7 points 3 weeks ago* (last edited 3 weeks ago)

1 + 1 + 1 + 1 + 1 + 1 + โ€ฆ = 1 + (-1) + 2 + (-2) + 3 + (-3) + 4 + (-4) + 5 + โ€ฆ

You forgot -5+6 on purpose.

spoiler
"In the expression on the right, all the terms cancel out"

You forgot the last one which is equal to the sum on the left.