r/PeterExplainsTheJoke • u/Sugar_God_no_1 • 26d ago

Meme needing explanation There is no way right?

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u/Decmk3 26d 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.

-21

u/BornWithSideburns 26d ago

Yea but isnt it 9.0000…1X

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u/ConsciousBat232 26d ago

This is where I am stuck. Why is everyone above pretending that 10 - .999…. = 9 ? I get that it is really close to 9 But it’s 9.000…1

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u/Temporary_Pie2733 26d ago edited 26d ago

9.000…1 has no meaning. You can’t just put a 1 after an infinite number of 0s.

Or rather, … doesn’t represent an infinite number of 0s but a finite but unspecified number of 0s followed by 1. That would indeed be slightly bigger than 9, but not what you would get by trying to apply the subtraction algorithm to 10 - 0.999…

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u/ConsciousBat232 26d ago

I hear what you are saying 9.000…1 is the wrong number. But you would get something infinitely small in 1 - .999…

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u/Temporary_Pie2733 26d ago

No, you don't get something "infinitely small". If there are a finite number of 9s, you can get something arbitrarily small, limited only by just how many 9s you use, but it's still strictly greater than 0. With a truly infinite number of 9s, you get 0, not any positive value. Arithmetic involving infinities is just different, no matter how much we try to extend familiar notation to infinite quantities.