What is infinity?

If universe is conceptualized as a binary string (not related to string theory) - which can be done if we assume universe to be nothing but the states of all that which make up universe from the start of the universe to now. Is that string infinite? Infinity is quite a vague concept and that resides only in our minds as something which goes forever like a line or series of numbers. What rigourous mathematical significance does infinity hold. If infinity is vague then so is infinitesimal. If there is no infinity, there is no infinitesimal and then that means there is no circle. Mathematical induction doesnt prove that a rule is applicable for all numbers but only that if we assume it is applicable for a number, and if it can be proved that it is also applicable for the next number - thus we can keep extending this to large numbers one number after another as much as we "wish". Now where does infinity come here?

Godel, Cantor, Turing, Chaitin all depend on that vague definition of infinity for all their theorems and discoveries to be true. Einstein and newton are different. We can have a discrete theory of general relativity or mechanics if we can use discrete calculus based on very small numbers which is not exactly infinitesimal. So all physics wont go flat but all theorems which depend entirely on the concept of infinity that it goes on forever would have a big problem. The diagnolization routine of cantor, on which all incompleteness theorem variations of godel, turing and chaitin depend on, is based on the fundamental concept of infinity. If we replace the infinity by very huge numbers these theorems will fall flat but that wouldnt entirely be the case with all other laws of physics though there needs to be considerable thought in framing laws of finite physics or discrete physics.

Boundaries like speed of light, minimum temperature, uncertainity principle (though different from other two) needs to be looked at as they are limits somewhat similar to the ones posed by godel, chaitin and turin. They like incompletness theorem might hold some clue into the true nature of real infinity.