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 Nov 27 accepted How to reconcile the existence of the least upper bound? Nov 26 comment How to reconcile the existence of the least upper bound? But, after all, if my intuition will refuse accepting this fact, I will have to accept it as a given. John von Neumann said: "In mathematics we don't understand things. We just get used to them." Nov 26 comment How to reconcile the existence of the least upper bound? When you say that $B$ has the form $[a, \inf)$ or $(a, inf)$, you assume the existence of the greatest lower bound in real numbers. Which is easier for $B$ -- I agree -- because $B$ is like an interval and $S$ is like a set of dots. But still it is not intuitive that there must be a real that is the greatest lower bound for $B$. Nov 26 asked How to reconcile the existence of the least upper bound? Nov 26 asked Compare a non-computable real number to a rational Sep 29 asked Textbook on calculus with the best application exercises Jul 25 awarded Nice Question Jul 5 accepted Factor a cubic polynomial Jul 5 asked Factor a cubic polynomial Jan 28 awarded Popular Question Jan 2 awarded Yearling Dec 9 awarded Caucus Oct 26 accepted Is it a wrong exercise in Pinter's Algebra? Oct 26 comment Is it a wrong exercise in Pinter's Algebra? No, this question is supposed to be proved. Oct 26 revised Is it a wrong exercise in Pinter's Algebra? added 28 characters in body Oct 26 revised Is it a wrong exercise in Pinter's Algebra? added 2 characters in body Oct 26 asked Is it a wrong exercise in Pinter's Algebra? Oct 17 comment Solving an exercise in Pinter's Abstract Algebra I still don't see how to show that for any $x \in H$, there is $y \in H$ such that $aya^{-1} = x$ (given that $aka^{-1} \in H$ for any $k \in H$). Oct 17 revised Solving an exercise in Pinter's Abstract Algebra edited body Oct 17 revised Solving an exercise in Pinter's Abstract Algebra edited body