(1)No matter how easy or no matter how difficult operation it is,
despite the operation never ending,
are we able to look infinite process obvious ?
(2)Although we can not always show the function,
we have to always accept the existing of the function. is it obvious?
Axiom of choice asserts these are obvious and true.
2017/06/30
2017/06/22
axiomatic sets 37 (axiom of choice)
For any non-empty set $\mathcal{A}$ , there is a function $f$
which can pick up an element $a$ from every each set $A$ in $\mathcal{A}$.
The collection of all $a$ is a set, and $f$ is called a choice function.
Do you think it is obvious or a self-evident truth?
which can pick up an element $a$ from every each set $A$ in $\mathcal{A}$.
The collection of all $a$ is a set, and $f$ is called a choice function.
Do you think it is obvious or a self-evident truth?