Infinity isn't an integer or real number. It's an abstract concept, a different type of mathematical object. But it's useful, much of mathematics and modern technology would not exist today without the application of the idea of infinity. Don't listen to the extreme finitists on this board. They are mentally diseased.
>>3
To complete you post, messing around with infinity might only be a good idea if you are one of the people cursed blessed with the daunting holy task of finding a better foundation for mathematics that isn't affected by the various paradoxes inflicted by infinite sets. But yes, rejecting infinity altogether would make it impossible to deal with calculus or Taylor series, for example.
>>6
If there is no infinity, then numbers must be finite. If numbers are finite, then there must be a largest or final number. What would that number be?