# Definition talk:Finite Extended Real Number

It's not the numbers themselves that are extended but the set $\R$. Therefore the term "extended real number" is spurious. A real number in $\overline \R$ is still the same real number as it is in $\R$ -- it does not change into a new "extended" form of itself when the set it is in is extended to contain two extra elements.

Therefore the concept of a "finite extended real number" seems to me to be spurious. On the other hand a "finite real number" is indeed a useful concept -- it is an element of $\R$, that is, an element of $\overline \R$ which is neither $-\infty$ nor $+\infty$.

Therefore it makes sense to me to rename this to "Finite Real Number".

Am I talking sense, or is there a subtlety I'm missing? --prime mover (talk) 13:51, 1 March 2014 (UTC)

- Well, the question we must ask ourselves is whether we want to save clarity of intention or sacrifice it for linguistic accuracy. I mean, we could call it "Finite Extended-Real Number" but it'd be a stretch. OTOH, "Finite Real Number" is downright strange and non-descriptive, so I'm definitely against that. — Lord_Farin (talk) 15:04, 1 March 2014 (UTC)

- Okay I'll leave it -- the maths this underpins is somewhat out of my expertise anyway. --prime mover (talk) 19:15, 1 March 2014 (UTC)