### Questions (127)

 5 What does Paul Halmos mean here? 5 Quantifiers in first-order logic 4 Show that the positive solution of $a = \tanh(ax)$ satisfies $\frac{1}{1-a^2} > x$ 4 What form of choice is "every Dedekind-finite set is finite" equivalent to? 4 How can I prove that every infinite set has a countably infinite subset using only the Axiom of Countable Choice?

### Reputation (1,677)

 +10 Constructing regular $mn$-gon if $m$-, $n$-gons are constructible +10 Deriving the addition and product on $\mathbb C$ +10 How to show that $(n\mathbb Z+a)(n\mathbb Z+b) = n\mathbb Z + (ab)$? +10 Which algebraic statements are preserved by isomorphisms?

 1 Terence Tao Exercise 5.4.3: Integer part of $x$ proof.

### Tags (110)

 1 analysis × 4 0 real-analysis × 10 0 set-theory × 19 0 ordinary-differential-equations × 7 0 first-order-logic × 16 0 general-topology × 7 0 logic × 15 0 linear-algebra × 5 0 elementary-set-theory × 13 0 calculus × 5

### Bookmarks (47)

 824 The staircase paradox, or why $\pi\ne4$ 159 Discontinuous derivative. [duplicate] 154 Most ambiguous and inconsistent phrases and notations in maths 136 Can you raise a number to an irrational exponent? 112 What are the Axiom of Choice and Axiom of Determinacy?