Permalink Submitted by Leslie.Green on September 11, 2018

Define (phi) as the infinite number of counting numbers, and allow (phi) to behave as a normal number.
A hierarchy of infinites is then as follows:

(phi)² = number of (positive) reals
0.6 x (phi)² = number of (positive) rationals
2x (phi) = number of integers
(phi) = number of counting numbers
(phi)/2 = number of even counting numbers
ln( phi ) = sum of the infinite harmonic series

These are all "infinite" values, but some are much large than others.

## Different Infinites

Define (phi) as the infinite number of counting numbers, and allow (phi) to behave as a normal number.

A hierarchy of infinites is then as follows:

(phi)² = number of (positive) reals

0.6 x (phi)² = number of (positive) rationals

2x (phi) = number of integers

(phi) = number of counting numbers

(phi)/2 = number of even counting numbers

ln( phi ) = sum of the infinite harmonic series

These are all "infinite" values, but some are much large than others.

http://lesliegreen.byethost3.com/articles/infinities.pdf