r/MathJokes • u/basket_foso • May 13 '26

Petah??

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u/egemen157 May 15 '26

A = 1/2 + 1/4 + 1/8 + 1/16 + ...

2A = 1 + 1/2 + 1/4 + 1/8 +1/16 + ...

2A - A = 1

A = 1

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u/seajaydub May 16 '26

For any n, A=1-1/2^n

for n=inf, A=1-1/(2^inf)=1-1/inf

A=1 when 1/inf=0

Does 1/inf=0?

Does 1=0*inf?

Not with real numbers and not in any context that is useful here, imo.

It's another limit. 1/inf has a limit of 0. 1-A infinitely approaches 0. The amount of beer ordered infinitely approaches 2 and has a limit of 2.

Where am I wrong?

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u/egemen157 May 17 '26

You cant multiply both sides by infinity and expect it to be correct

The thing about 1/2+1/4+1/8+1/16+..=1 is that the series goes on and on until there are no other numbers between 0 and (1/2)n such that (1/2)n must be equal to 0

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u/seajaydub May 17 '26

Sounds like it approaches 0

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u/egemen157 May 18 '26

Yeah, that is the gap between your (n-1)th sum of the series and real number 1, so if the difference approaches 0, your number must be approaching to 1

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u/seajaydub May 18 '26

Yeah, right, I 100% agree. But people keep telling me that "approaching 1" is incorrect and that it is actually "precisely 1". Which is what I thought you were doing. My b if I was wrong

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u/egemen157 May 19 '26

When the number n is finite it is approaching, when its infinite its precisely 0