How many real numbers exist? New proof moves closer to an answer

Re:How many real numbers exist? New proof moves closer to an... by ummonk on Saturday July 17, 2021 @07:37PM (#27869663)

"Then you should be able to come up with a function that assigns a natural number uniquely to each real number. Of course if you tried that I could immediately name you a real number, or a pair of them, for which your rule doesn't work"

I can give you a function that will never output the same natural number on any two real numbers unless those two real numbers are equal.

My function outputs the binary value of the Unicode encoding of the description of the number that you provide.

Go ahead, name me a pair of real numbers for which my rule doesn't work.

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Re:How many real numbers exist? New proof moves closer to an... by chmod775 on Sunday July 18, 2021 @12:01PM (#27874001)

The thread already went down that line of argument, you can take this comment as an response to yours: https://news.ycombinator.com/item?id=27851171

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Re:How many real numbers exist? New proof moves closer to an... by btilly on Monday July 19, 2021 @11:35AM (#27883768)

And, as I pointed out there, that comment remains wrong.

See https://news.ycombinator.com/item?id=27859355 for why.

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Re:How many real numbers exist? New proof moves closer to an... by ummonk on Sunday July 18, 2021 @05:45PM (#27876981)

Upthread you said: "Of course if you tried that I could immediately name you a real number, or a pair of them, for which your rule doesn't work."

That is false - you're actually unable to name these numbers for which the rule doesn't work. Instead you're just insisting we accept on faith the existence of these unnamable numbers.

[ Parent | on HN ]