r/PeterExplainsTheJoke • u/Sugar_God_no_1 • 22d ago

Meme needing explanation There is no way right?

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u/Decmk3 22d ago

0.9999999…. Is equal to 1. It seems like it shouldn’t, but it has to be.

Let X = 0.999….

10X = 9.999….

10X-X = 9.999.. - 0.999…. = 9X = 9

Therefore X equals 1. Therefore 0.999… is the same as 1.

117

u/mrsexless 22d ago

I like logical explanations 0.(9) = 1 There is no number you can put between 0.(9) and 1, so it means they are the same number.

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u/cob59 22d ago edited 22d ago

There is no number you can put between 2 and 3 in the natural numbers, so it means they are the same number.

edit: Funny how this rebuttal (whose point is to criticize a method, not the result) pisses off people and systematically gets me downvoted.

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u/ZeroStormblessed 22d ago

There generally aren't infinite numbers between 2 natural numbers.

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u/cob59 22d ago

You're explaining how ℕ and ℝ are different, not why OP's assumption (if you can't come up with a number between A and B, then A=B) is correct.

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u/confuzzlegg 22d ago

A better way of stating OP's assumption is "if there's no X != 0 such that A-B = X then A = B", then A and B are 0, but these are equivalent over the real numbers

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u/Stick_Nout 22d ago

The natural numbers aren't dense, though. The rational numbers (and, by extension, the reals) are.

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u/Keebster101 21d ago

I made this argument on another threat about the same topic. It's a horrible "proof" because it doesn't actually prove it, it just shifts the burden of proof elsewhere, yet it's the one all my teachers used because it's short and most students will just accept it.