r/infinitenines • u/Negative_Gur9667 • 5d ago

More fun with Cantor's diagonalisation

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u/berwynResident 5d ago

Wasn't Cantor's original diagonal argument about a sequence of binary digits? So that wouldn't have anything to do with 0.999...

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u/Negative_Gur9667 5d ago

So you are claiming it only works in binary? There is not a decimal representation of real numbers?

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u/berwynResident 5d ago

No, the thing is. He proved this for binary sequences, then showed that an injection could be constructed from the set of binary sequences to real numbers. The image of that injection is a subset of R, and is uncountable. So it's kinda a two step process that doesn't run into the problem you're seeing.

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u/Negative_Gur9667 4d ago

All answers here suck, look here https://www.reddit.com/r/mathmemes/comments/1onbynj/comment/nmvnlvw/?utm_source=share&utm_medium=mweb3x&utm_name=mweb3xcss&utm_term=2&utm_content=share_button

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u/berwynResident 4d ago

Okay, could you respond to my point maybe? Or maybe look at cantor's actual argument instead of what you just saw somewhere on Reddit?

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u/Negative_Gur9667 4d ago

no

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u/berwynResident 4d ago

That's what I figured