>>12393552>>12393552>If the finitist framework is wrong, then there's no hope for the infinitists.You may not know this, there are theorems which are provable in ZF which are not provable in ZFC. So it may be that the axiom that allows infinite sets corrects some defect that finitist set theory has.
So its not necessarily the case that if finitism is wrong then infinitism is wrong.
>>12393552>I meant if you're talking about an actual set of strokes written on the board, that doesn't imply the strokes need to be neatly ordered in a string.In this case, a string is a set of strokes.
You could represent that string as an ordered n-tuple if you wanted.
Take ||||||||||. Assume each stroke is unique, then we assign it a number in its place, so we can uniquely identify it, which becomes 123456789. Which is the same as counting the place of each stroke. Then a string is equal to the ordered n-tuple (1,2,3,4,5,6,7,8,9)
If I had:
||||||
|||||||||
||||||
Three strings of strokes. I could have the set of all those strokes, or i could one set per string, and the set of those 3 strings.
A set is actually pretty well defined as an abstraction from the real-world version, but they dont teach much about bolzano or cantor.
Generally they teach children about venn diagrams, which is pretty much what a set is.
The set of all men. The set of all Greeks. The set of all Greek men is the intersection in a venn diagram. Pretty simple stuff
