Quote (Voyaging @ May 14 2012 12:35pm)
No need to be angry

We both need to keep in mind, however, that mathematics, ESPECIALLY math dealing with infinities is widely open to interpretation and there are loads of different schools of thought. Philosophy of mathematics is a real discipline.
In her book Philosophy of Set Theory, Mary Tiles characterized those who allow countably infinite objects as classical finitists, and those who deny even countably infinite objects as strict finitists.Not angry m8. Math is hardly an emotional subject ^^
I'm talking about mathematics, not the philosophy of mathematics.
Actual practicing mathematicians rarely espouse fringe views such as finitism as it makes much of the higher mathematics impossible (or very different and not really applicable, or just unnecessarily complicated)
The real numbers don't even exist in a finitist perspective... the best you could use is the computable real line.
There's really no "interpretation" to it.. math is about proofs... if you want to deny that the real numbers exist you're free to do so.
But if someone accepts that real numbers exist then they also accept that they are uncountably infinite (and so a higher cardinality of infinity than countable infinities) because it has been proven.
Example of non-computable real number (doesn't exist in finitism)
http://en.wikipedia.org/wiki/Chaitin%27s_constant(Interestingly, for every programming language the number of possible programs is countably infinite, and thus the computable numbers are countably infinite since each can be printed by some computer program to however much accuracy you want)