Notation: the set of two-element subsets of $\Bbb N$

Question

Let $\{a,b\}\subseteq \Bbb N$. Is there a special name or notation for sets of this type, for example $\Bbb N^{2\ge}$? Any subset size may be used, but the specific size and denoting that order does not matter is part of my interest in this notation, i.e., subsets of size $n$ of set $X$.

Particularly inspired by this question: Produce unique number given two integers.

Answer 1

One common notation is $[X]^2$, or more generally, $[X]^{m}$ where $m$ is any cardinal number (finite or infinite) is the set $\{A\subseteq X\mid |A|=m\}$. Similarly we can define $[X]^{<m}$.

In this case, $X=\Bbb N$.

Answer 2

I'm a fan of:

$$\binom{\mathbb{N}}{2}$$

Answer 3

My preferred notation for $k$-element subsets of $X$ is $\binom{X}{k}$. I use $2^X$ for all subsets of $X$ (the power set). For something like subsets with 2 or more elements I would just write $\bigcup_{k \geq 2} \binom{X}{k}$.

Of course my area is combinatorics which explains my liking of this notation.