### Questions (765)

 19 With this definition of completeness, Gödel's Incompleteness result seems not surprising, so why it was back then? 13 Open Sets in Product Topology. 11 The notation $\prod_{g\in G} g$ for a finite group not well-defined. 10 Show that a semigroup with $aS \cup \{a\} = bS \cup \{b\}$ and $Sa \cup \{a\} = Sb \cup \{b\}$ is a group 10 Simple and intuitive example for Zorns Lemma

### Reputation (8,290)

 +5 Simple and intuitive example for Zorns Lemma +5 Let $X$ and $Y$ be Banach spaces, show that if they are isomorphic, then $X$ is reflexive iff $Y$ is reflexive. +10 How to find the number of anti-symmetric relations? +10 If two elements are in the same orbit, show the stablilizer groups of those elements are conjugate subgroups

### Answers (90)

 20 Can mathematics get from other sciences what it got from physics? 10 How are simple groups the building blocks? 7 Show that a semigroup with $aS \cup \{a\} = bS \cup \{b\}$ and $Sa \cup \{a\} = Sb \cup \{b\}$ is a group 7 What's the point in being a “skeptical” learner 5 Generalization of $|HK|=\frac{|H||K|}{|H∩K| }$, where $H,K$ are finite subgroups

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 44 abstract-algebra × 436 20 finite-groups × 233 43 group-theory × 317 20 philosophy × 3 27 soft-question × 3 20 biology 24 book-recommendation × 3 10 regular-language × 15 21 computer-science × 19 10 simple-groups

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