On Friday, June 14, 2013 3:04:22 PM UTC-7, Virgil wrote: > In article <firstname.lastname@example.org>, > > Zeit Geist <email@example.com> wrote: > > > Definition: A set, X, is infinite iff there exists a function, F and a > > > subset Y of X, such that F: X --> Y and F is onto. > > > > X need only be infinite if the set Y is a PROPER subset of X. >
Y c X is meant to read "Y is a proper subset of X" Just like a < b reads as simply "less than" when a and b are real numbers.
> > > Theorem: In ZFC, if X is an infinite set, then for all n e N, there > > > exists a Y c X such that there is function that map X onto Y. > > > > In ZFC, if X is an Finite set, then for all n e N, there > > exists a Y c X such that there is function that map X onto Y. > > Namely whenever Y = X >
> > > Theorem: In ZFC, if X is an infinite set, then for all n e N, the > > > cardinality of X is greater than n. > > > > That one is both correct and meamingful. >
All are correct with clarification. When the improper subset of Y = X is permitted, I, and most I believe, write Y c= X.
I try to be more clear in the future. When writing this i thought somebody might say this. All good.
> > > This is ZFC. If you want to create a consistent theory that is > > > In opposition to ZFC, feel free. This, however, will NOT effect the > > > validity of ZFC. > > > > If you want to create a consistent theory other > > than ZFC, try ZF. > > > > Standard mathematics is almost all compatible with ZF, with or without C. > > A very large part of standard mathematics is incompatible with WM's > > WMytheology. >
I never said he was coming anywhere close to creating an alternative consistent theory of any sort.