(November 26, 2022 at 5:54 pm)LinuxGal Wrote: Not so, since x = 0.999... has an upper bound as the decimal expansion continues without limit, but x = 1+2+4... diverges.
True. In your case, though, you are performing the same trick - it is just that the additional digit you shifted in is an infinitesimal instead of a large value.
I'm not sure if your proof is valid, but of course one can get as close to correct as you like.