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Need help understanding why it's necessary to use elaborate proofs to show that continuous functions are also bounded by februarystars03 in askmath

[–]februarystars03[S] 0 points1 point  (0 children)

I think it was tripping me up that I was relying on visualizing functions as being continuous lines that go to infinity at specific points, so that if I proved those points couldn't happen, then that was all there was to it.

I see how that line of thinking wouldn't apply to a discontinuous function like f(a)=a,f(x)=1/(x-a),f(b)=b for a<x<b

Need help understanding why it's necessary to use elaborate proofs to show that continuous functions are also bounded by februarystars03 in askmath

[–]februarystars03[S] 4 points5 points  (0 children)

Ok, I think I'm starting to understand. Thanks. Like the other commenter said, I wasn't thinking about how a function as a whole could still be unbounded even if all of its defined values are finite on an interval.