Many schools of math philosophy do without infinity:
http://en.wikipedia.org/wiki/Finitism
http://en.wikipedia.org/wiki/Ultrafinitism
http://en.wikipedia.org/wiki/Mathematical_constructivism
http://en.wikipedia.org/wiki/Intuitionism
Many schools of math philosophy do without infinity:
http://en.wikipedia.org/wiki/Finitism
http://en.wikipedia.org/wiki/Ultrafinitism
http://en.wikipedia.org/wiki/Mathematical_constructivism
http://en.wikipedia.org/wiki/Intuitionism