If I say "let $x_0$ be a point of global maximum...", am I using axiom of choice?
27025
How do I choose an element from a non-empty set?
48030
Axiom of Choice: Where does my argument for proving the axiom of choice fail? Help me understand why this is an axiom, and not a theorem.
153935
A weaker Axiom of Infinity?
65308
Axiom of Choice: Family of non-empty sets mutually disjoint or not?
70262
Can the axiom of choice be used to define the real numbers?
8851
if $(x_0,y_0)$ is local extrema in $ax^2 + by^2 + cxy + dx + ey + l$ then its global too.
148266
Let $f:X\to X $ be continuous. Does $f $ have a fixed point when $X=[0,1)$ or $X=(0,1) $?
152272
Can you explain the "Axiom of choice" in simple terms?
65371
Does $2^X \cong 2^Y$ imply $X \cong Y$ without assuming the axiom of choice?
73526
The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
118573
Why is the Axiom of Infinity necessary?
34045
3 Statements of axiom of choice are equivalent
29180
If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
77855
Prove that if $A$ has a maximum, then the maximum must be the supremum
5313
Existence of how many sets is asserted by the axiom of choice in this case?
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
156235
Are $x \cdot 0 = 0$, $x \cdot 1 = x$, and $-(-x) = x$ axioms?