Ambiguity about Real numbers

[gezeta-id]

Note: Real numbers are also finite, as in, not infinite.

I don't think this expresses well what it is trying to express. I'm guessing that it is referring to the check && isFinite(k) to exclude ∞ (Infinity) from ℝ, which in itself is correct, as infinity is not a Real number. But, saying that "infinity is not a real number" is different from saying that "real numbers are finite". This second way of saying it may confuse people with the fact that "ℝ is of infinite size", i.e. that "there are infinite real numbers".

What I think may mark the difference is that, in english, "Real numbers" usually refers to all of them as a whole, while "A Real number" refers explicitly to any individual Real number. I think a better way of saying this could be something along the lines of "Note: Infinity is not a Real number" or maybe "A Real number is also finite, as in, ∞ ∉ ℝ").