>between any two rational numbers there exists an irrational number
>Between any two irrational numbers there exists a rational number
>The rationals plus the irrational creates the reals
Someone explain how this doesn't permit an isomorphism between the natural numbers and the reals. For example,
>{0,irrational,rational,irrational,...}
Whereby you can then map odd integers to irrational numbers and even integers to rational numbers.
>Okay anon what are those irrational and rational numbers?
Easy. Let's recast the set as
>{0,epsilon_i,epsilon_r,_2epsilon_i+ epsilon _r, 2epsilon_i + 2epsilon_r,...}
Where epsilon is the unique infinitesimal between two (ir)rational numbers.