Another math question

[txags911]

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

 False.   0.9999~ is not an irrational number any more than 0.333~ is.  It is 3 * 0.3333~ (or 3 * 1/3) (or 1)

 An infinitely repeating number is not necessarily an irrational one.  That's the mistake you made.

 Incidentally, the true proof is that between any two non-equal REAL numbers, there is an infinite number or other real numbers between them.  So if  0.999~ and 1 are not the same, you should be able to name at least 1 number between them.