Is it mathematically correct to define the following:
- $[0, \infty] \equiv \displaystyle \lim_{n \to \infty}{[0, n]}$
- $[0, \infty) \equiv \displaystyle \lim_{n \to \infty}{[0, n)}$
More generally, I'm concerned with the "boundary" between the arbitrarily large and the notion of infinity. Is there some good philosophical treatment of this sort of conundrum?