[vcxy]

> when people say "infinity is not a number" they generally mean aleph-0

Sure, maybe. I think saying "infinity is a number" is wrong regardless. I'm happy with aleph-0 being a number, and I'm happy with it having a label of infinity. I'm just not happy with treating infinity as a single thing. We're totally on the same page in every way that matters though. I'm also certainly with you on questioning Retric's comment for a number of reasons, haha.

edit: Actually...I'm not so sure they mean aleph-0. I think frequently they mean the infinity of the extended real line. Maybe it depends on the context of the conversation.

[jjgreen]

It's actually a great ice-breaker for first-year maths undergrads, when talking about limits or whatever drop in "... to infinity and beyond!", laughter follows, then say "You think I'm joking? Put down your pens ..." and informally outline the aleph hierarchy, then things get rather quiet.

[vcxy]

Ahh I wish I had gotten the chance to interact with new math majors more often. In grad school most of my students were engineering majors. I'm not super likely to end up back in academia. My published research is...sparse. I have post-doc opportunity but it's not the greatest, and the route to life stability is not so clear. Are you a math professor?