JHawkNH said:
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. |
The rational numbers are a countably infinite set which when combined with the irrational numbers forms the real numbers ...
| txags911 said: 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. |
You're correct in that not all repeating numbers are irrational, but 0.999... is an irrational number
You can not express it as a ratio of two other numbers thus it is irrational.
Anyways ... I'm taking my math degree in pure mathematics and leaving this thread ...
