A student asked me “Is infinity a number?” while I was introducing limits. My immediate response was “infinity is a concept” and I started talking about vs. . I didn’t really know where I was going with that though, so I let the students debate for a bit and finally related the whole conversation back to the problem at hand. The discussion was interesting, but other than acknowledging the difficulty of comprehending infinity, I didn’t contribute much (which is usually good, but I certainly didn’t provide clarity).
How do you define infinity?