Thanks for asking. Not sure I have much more to say, but:
I find the concept of infinity quite unintuitive because in everyday life the size of the whole is not equal to the size of each of its parts.
As any non-null number multiplied by infinity equals infinity, 10^-10^10^10^10^10^10^10^10^10 of infinity is exactly equal to infinity.
This applying to something in the real world seems non-sensical to me.
According to this page of Wikipedia, the axiom of choice is equivalent to the following. “Given any family of nonempty sets, their Cartesian product is a nonempty set”.
In the same way that we cannot arrive to null energy from positive energy (since that would break conservation), we cannot arrive to empty sets multiplying non-empty sets.
That being said, my intuitions with respect to the axiom of choice are more or less agnostic.
Hi Bruce,
Thanks for asking. Not sure I have much more to say, but:
I find the concept of infinity quite unintuitive because in everyday life the size of the whole is not equal to the size of each of its parts.
As any non-null number multiplied by infinity equals infinity, 10^-10^10^10^10^10^10^10^10^10 of infinity is exactly equal to infinity.
This applying to something in the real world seems non-sensical to me.
According to this page of Wikipedia, the axiom of choice is equivalent to the following. “Given any family of nonempty sets, their Cartesian product is a nonempty set”.
I find this decently intuitive due to similarities with conservation of energy.
In the same way that we cannot arrive to null energy from positive energy (since that would break conservation), we cannot arrive to empty sets multiplying non-empty sets.
That being said, my intuitions with respect to the axiom of choice are more or less agnostic.