[Mindless2112]

> In real analysis, the projectively extended real line [...] is the extension of the number line by a point denoted ∞.

> The extended complex numbers consist of the complex numbers C together with ∞.

It may be an "extended number", but it is not a number.

[jacobolus]

If you can consider a “complex number” or a “transcendental number” to be a “number”, then there’s really no reason to not also consider ∞ to be a number.

In general, the boundary of the category of ideas (if you like, elements of some formal model) that can be called “numbers” is a very fuzzy and arbitrary one.

Some people might reject as “numbers” anything other than the counting numbers 1, 2, 3, 4. Others might allow “negative numbers” or ratios. Still others are happy to include quaternions or infinite strings of digits output by some computer program. Meh.