Oh, and about 1/x, hell I knew I was missing something. I study Industrial Egineering and this is such a common case that I forgot to explain it properly. What convergence/divergence means is: If you take the 1/x function and add all the possible natural values for the function, does it aproach a certain number? This is 1/1 + 1/2 + 1/3+ ... You can check that 1/x aproaches no number, while 1/x^2 does (1/1 + 1/4 + 1/9 + ...). Anyway let's leave this apart, since it has nothing to do with the thread.
About the other two quotes, I don't know, we say that the result of 1^infinity is indeterminate (it is a different result depending on the function, not that it doesn't have an answer). And about infinite, is it a number? I don't think so. Which is the natural number that goes right before infinite? I can answer this for every number but infinity (because it's an idea, not a number).