r/HomeworkHelp • u/anonymous_username18 University/College Student • Jun 26 '26

Additional Mathematics—Pending OP Reply [Real Analysis] Closure of Sets

Can someone please help look over my proof of this theorem? I tried to get CoPilot to check, and it said my reasoning is incorrect, but I'm not quite following why. Any clarification would be appreciated. Thanks

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u/anonymous_username18 Jun 26 '26

Thank you - yeah, AI definitely isn't great with proofs, and I'll try to avoid it. I'm trying to self-teach some of this stuff, so it's hard to get direct help sometimes, but I see your point.

I appreciate the explanation - thanks again!

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u/Alkalannar Jun 26 '26

You're welcome.

For the record: come here and ask! Showing your work like you did is exactly what we ask for, and we're glad to help out.

So yes, your logic was right. I'd've gotten there quicker. Both u/FortuitiousPost and I went to the same place: every open ball centered at a limit point of E must have an infinite number of points of E in it, and so cannot be in U, which requires an open ball with only points of U (and so not points of E, since they're disjoint) in it.