Cantor's Theorem

Cantor's thm sets a cardinality to infinity, e.g. all infinities are not equal. As an example consider integers, they go from a negative infinity integer to a positive integer infinity so the set has an infinite number of elements.

But is there a 1 to 1 relation between the elements in the set of integers and the elements in the set of rational numbers? Cantor argued that an infinite number of rational elements existed between any two integer set elements. So the answer was no, the infinity of the set of integers was smaller (had a smaller cardinality) than the set of rational numbers. The set of rational numbers had a higher cardinality (aelph) than the set of integers.

The same can be said of the set of irrationals over rationals, and the set of imaginarys over irrationals.

Now to your problem---I really don't understand the fixation with Cantor

I see the following condition
if w(w)>1
then
w(w)<w(w)^n if n<1
w(w)=w(w)^n if n=1
w(w)>w(w)^n if n>1

if w(w)=1
then
w(w)=w(w)^n for all n

if w(w)<1
then
w(w)>w(w)^n if n<1
w(w)=w(w)^n if n=1
w(w)<w(w)^n if n>1

Rap

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