If you're going to nitpick this comment, you should note that infinity isn't on the number line and infinity != infinity, and dividing by zero is undefined
Also, you say NaN ("not a number") is "defined as a number" but Infinity is not. I would think every IEEE 754 value is either "a number" or "not a number". But apparently you believe NaN is both and Infinity is neither?
And you say 0 / 0 is "undefined" but the standard requires it to be NaN, which you say is "defined".
That's not true. For example: 0 == 0, but 0/0 != 1.
(See also +Infinity, -Infinity, and -0.)