The function is a homeomorphism on R, so it preserves its topological features.
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By using 🍊 to rate how good this post is(out of 5), i made it a metric for how good this post is
I can answer the question. No.
Look at this shmuck, using the supremum of a continuous function on a closed interval when it clearly achieves a maximum. I bet they’ll feel real embarrassed about that one when they’re falling asleep years from now.
Christ, it’s like people just don’t even give a fuck about the extreme value theorem anymore?
Nyar!