/sci/ - Science & Math

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https://en.wikipedia.org/wiki/Intermediate_value_theorem#Relation_to_completeness

Again, I don't see how you guys aren't getting this. Without assuming completeness of the reals you cannot use the intermediate value theorem. That's why I said your interval cannot contain [math]2^{1/2}[/math]. That's why I kept repeating that using Dedekind's fundamental theorem is how you would go about it.