>>16585539
>Did you notice that the only thing "wrong" with OP's post is that it defines infinite decimals in a nonstandard way?
A proof that starts with an inconsistent set of assumptions with the context can prove literally anything. They describe infinite decimals in a way that simply doesn't behave like real numbers.

>It's pretty obvious if you read through OP's post that he knows how to prove 0.999... = 1 under standard definitions.
This is not obvious to me at all.

>Fortunately none of that is necessary to explain what 0.999... is supposed to represent

** Proceeds to start an (admittedly good) epsilon-n proof in the same message**

>I bring up eighth graders because this is approximately when concepts like 0.999... are normally introduced to students, and things should be explained as simply as possible. OP keeps things relatively simple, why can't you?

I can own up to the fact I included more theory than was strictly necessary to prove 0.999... = 0. It did occur to me to show this was true in the rationals, but OP's post was about real numbers, so I chose that direction.

I have had professors describe two kinds of mathematicians: those that prefer to solve an individual problem quickly and directly, and those who prefer to slowly lay the groundwork that trivializes whole classes of problems. If you and I were trying to reach a tree on the opposite side of a deep chasm, your explanation is more akin to throwing a grappling hook towards the tree and swinging across. Mine is more akin to filling the chasm with gravel and walking across. Both approaches have their merits.

> Responding to that by regurgitating what you learned in college about real numbers is something an LLM would do.

Seems uncalled for. It's not like I'm spewing copypasta here. What I learned about real numbers in college was a skillset earned through long hours of practice. I'm not reciting proofs; I'm reconstructing them from base principles.

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