is every non-terminating real growing

if 0.999... and π are always growing. is every non-terminating real?

say e,√2, φ, 3/7, etc. are all of these "growing" without limit?

if so, after what amount of time are they equivalent to their expected value?

at what poimt does sqrt(2)^2 = 2 if sqrt(2) is growing?