The Numbers have broken in the roof, what sort of rain will leak in?

[shaolin_beaver]

A 'square number' is one that is the square of an integer.

There are 10 square numbers between 1 and 100    (10%)

There are 100 square numbers between 1 and 10,000    (1%)

There are 1,000 square numbers between 1 and 1,000,000    (0.1%)

There are 1,000,000,000,000 square numbers between 1 and 1,000,000,000,000,000,000,000,000    (0.0000000001%)

Yet...

If

Comments

[raisedonadiet]

Some numbers are both though. 4 is a square number, and has the square 16, just like 9 and 81. So is there a 2:1 ratio?

[shaolin_beaver]

This is correct, I got my thinking mixed. There are as many squares as there are integers. There are more integers than there are integers with irrational roots since squares exist.

Therefore there are more squares than not squares.

Gah