The meaning of the symbol $\ni$

Question

I was solving an inequality problem. Just like we write our answer in the form $x\in (a, b)$, I was just wondering if we can write it like $(a, b) \ni x$. Does it make any sense? I've not seen such notation in book or anywhere but got it on my own.

Can anyone tell me what's the use of this symbol and is writing $(a, b) \ni x$ valid?

Answer 1

$\ni$ is very valid, although not as commonly used as $\in$. One could certainly write something like

Take a real number $x$ and an open interval $(a,b)\ni x$.

It would be really strange to say

Take a real number $x$ and an open interval $x\in (a,b)$.

because grammatically it looks like $x$ is this interval. I think most people go for

Take a real number $x$ and an open interval $(a,b)$ such that $x\in (a,b)$.

which is more correct than option number 2, but significantly longer than option 1. I prefer the first one personally, although some times I go for option 3 anyways to conform to the more common phrasing.