I was not able to confirm this bug fact, hard to search a math theorem without a name. If anyone knows what this theorem is called and if it is true id be glad to know
this post was submitted on 22 Aug 2023
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https://math.stackexchange.com/questions/88300/if-fx-is-continuous-on-a-b-and-m-max-fx-is-m-lim-limits-n
Not a theorem really just homework problems