Another math question

[JHawkNH]

HappySqurriel said:

txags911 said:
Put a simpler way, if they are not the same number, you bby definition should be able to tell me one number that comes between 0.9999~ and 1. If you cannot do that, they are by definition the same number.

False ...

Between any two rational numbers there is an uncountably infinite number of irrational numbers between them, your irrational number 0.999... is between 0.99999 and 1.0

That is incorrect.  The irational numbers are a different number set then the rational numbers.  By definition because of this you can not find an irrational number between to rational numbers.