On Mar 14, 12:07 am, "DavidW" <n...@email.provided> wrote: > Frederick Williams wrote: > > DavidW wrote: > > >> I don't dispute that. Nevertheless I will never run out of integers > >> to pair with any selection of real numbers you care to nominate. By > >> definition you cannot exceed infinity. > > > By _what_ definition? There may be dictionary definitions according > > to which infinity cannot be exceeded, but in mathematics there are > > many infinities, for example > > > omega and omega + 1 > > or > > aleph_0 and 2^aleph_0; > > > in each case the second exceeds the first. > > Because you and other Cantor disciples have simply asserted it so. It's an > axiom.
*** No, it's not. It's a logical deduction from a logical definition: we say the cardianl of set A is bigger than the cardinal of set B if there's a 1-1 function from B to A and there is NOT a 1-1 function from A to B.
Thus, it is easy to show that the cardinal of the real numbers R is bigger, according to the above definition, than the one of the natural numbers, N.
As you see, the above is just mathematics, logical deduction and fun. All the rest is ranting and whimsical behaviour.