How to prove that the set $A = \left\{ {p:{p^2} < 2,p \in {\Bbb Q^+}} \right\}$ has no greatest element?
4552
Choice of $q$ in Baby Rudin's Example 1.1
8494
Proof Check: Number of elements of $\mathbb{F}_{p^{n}}$ of the form $a^{p}-a$ for some $a \in \mathbb{F}_{p^{n}}$.
137511
Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$
116527
Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
12701
Perfect set without rationals
75039
Smallest positive element of $ \{ax + by: x,y \in \mathbb{Z}\}$ is $\gcd(a,b)$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
86505
Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$
144623
Can one avoid AC in the proof that in Noetherian rings there is a maximal element for each set?
55023
if $A$ subset of $B$ then $P(B)-P(A)=P(B\setminus A)\ge 0$
858
Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$?
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
42603
How can I prove that the cadinality of a set minus a finite number of elements of it is still the same as the original set?
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
43024
Well-ordered sets, properties of an element that is not largest in the set
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
93771
Prove that for any set $A$ there is some $x \notin A$