Can infinity be defined as rational or irrational - and why? - Answers

Infinity is not just really big number - and consequently the concepts of rational vs irrational cannot be applied to it. It is a marvelously useful concept with great utility in mathematics but don't confuse it for being the same as a number that we could write out and categorize just because we have a symbol for representing it. When you stick infinity into an equation you get things like "limits" rather than a fixed answer; for example - for the function f(x) = (x-1)/x, if x = ∞ you don't actually get a value for the function- rather you get a limit that it approaches as x goes off to infinity; in this case the limit as x approaches infinity is 1. For the function f(x) = (x-2)/x, the limit as x approaches infinity is ALSO 1, and for the function f(x) = x/(x-1) the limit as x approaches infinity is .... 1. Obviously for any finite number they will not have the same value, but conceptually they all converge to the same value as you go to infinity. Hopefully this illustrates why you cannot apply the concept of rational vs irrational to "infinity".