I initiated the "0" and the "inf." threads. Wow, the "inf." finally halted at 100 responses!

There was one thing that never came up. Some mathematicians went into "special analysis" with this particular view: the entity "d" or "iota", d = 0.000...001. In other words infinitesimally small. And 0.999... + d = 1. Now, if someone insists that d = 0, well it would still be OK, since one could say that 0.999... + 0 = 1. Or?

I know one retired mathematician who doesn't disagree with 0.999... = 1, but he says that 0.999... + d = 1 is more correct, since it eliminates certain doubts that some have about it.

Anyway, since I first read "Flatland" many years ago, I've been fascinated with the concept of 4-space. I'm quite familiar with the tesseract, a similar figure for a tetraeder, etc. I have been wondering about a 4-space sphere. Can it be two spheres which coincide? Anybody know? I've been searching Wikipedia for an answer.