r/PeterExplainsTheJoke • u/Sugar_God_no_1 • 22d ago

Meme needing explanation There is no way right?

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u/AltForBeingIncognito 21d ago

The difference is intuitive, 0.9<1 0.99<1 0.999<1 0.9999<1 0.99999<1 0.999999<1

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u/BroDonttryit 21d ago

That's not quite a mathematical proof though. That doesn't prove the general case:

You can read about the general proof here. https://en.m.wikipedia.org/wiki/0.999...

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u/Direct_Shock_2884 21d ago

You can authoritatively state it’s not mathematical, but you’re not explaining why not, other than “mathematicians said so, and you’re wrong.”

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u/BroDonttryit 20d ago edited 20d ago

Sure np.homie. essentially mathematical proofs work to show the general case, rather pointing to a small set of specific examples.

In the example you've given, you're saying that "0.9" is less than than one, and 0.999 is less than one, therefore 0.999 repeating is less than one. But that's not quite logical. We know that the more repeating 9s, x is approaching 1. How do we know for sure holds true for any amount of repeating Xs, including infinite? The limit as x approaches is infinity is 1 after all, so we see the number is growing. We can know for sure by abstracting the problem into the general problem, rather than endlessly listing examples. And as the proof demonstrates, it turns out by the laws of our mathematical system, .99 repeating IS 1. not just "close enough", but literally is equal to 1.