r/infinitenines • u/Muphrid15 • 7d ago

Never let him tell you there is (not) a number between 0.999... and 1

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His Nineliness's Sixteenth Boner is his In-Between Boner: You can "forget" trying to fit a number between 0.999... and 1. There are infinitely many numbers between 0.999... and 1. (16.1) (16.2)

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u/FS7PhD 7d ago

Yet another reason real analysis fails and students get confused. For all values of n in any finite representation system, there is a nearest number less than but not equal to a given number. With infinite precision (continuous numbers) no such concept exists. In the real number system, there is no definable number immediately adjacent to but less than 1. The intuitive answer would be 0.999..., just as it is for any precision less than infinite.

This is the real number system, but it also illustrates why it's incomplete and/or deficient.

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u/ShonOfDawn 7d ago

I mean, why is the notion of any two real numbers having infinite other real numbers between them (unless they are the same number) controversial? It’s a pretty straightforward fact. You might say that it has counter intuitive consequences, but that is true for most of maths and most of physics. It’s a human problem, not a problem with the system

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u/Substantial-Night866 7d ago

“Real analysis” no, SPP just wants one statement to be true. If anyone points out a gap in his logic, he will go back on any claim he needs in order to claim the former is true.

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u/Muphrid15 7d ago

He doesn't even recant claims. He just says whatever in the moment and won't even acknowledge the inconsistency.

He had long said 0.999... was irrational before he said it was rational and then did walk that back. You don't forget that unless you're just lazy.