i am trying to understand the axiom of choice.

def from book: suppose that $\displaystyle C$ is a collection of nonempty sets. Then there exist a function. $\displaystyle f: C \rightarrow \bigcup_{A\in C}{A}$ such that $\displaystyle f(A) \in A$ for each $\displaystyle A\in C$.

isnt this trivially obvious becouse ex.

if $\displaystyle C = \{\{1\},\{3,4\}\}$ then $\displaystyle \bigcup_{A\in C}{A} = \{1,3,4\}$

and if $\displaystyle f = x$ then $\displaystyle f(\{1\}) = \{f(1) \in \{1\} \}$ and $\displaystyle f(\{3,4\}) = \{f(3) \in \{3,4\},$$\displaystyle f(4) \in \{3,4\} \}$

have i understod this correct?.

now what i dont understand is that certain mathematician refuses to use this theorem, they think that this theorem cant be trusted.

why?

also about latex, when i tried to see what the code would look like when i posted it, stuff like f(< fontsize = \{1.... appeard.

so i thought something was off with the size, so i marked the text and clicked on 2. that removed the problem.

maby this is a bug, in this sites latex interpreter.

also when i clicked size, the [size] parameters did not appear.