# First use of curly braces to denote a set?

I was wondering who was the first person to

• Use curly braces to represent a finite set. Exempli gratia, $\{1,2,3\}$.
• Use set builder notation. Such as $\{2n:n \in \mathbb{Z}\}$ to represent the even numbers. I am not sure if the colon or vertical pipe is the original form for set builder notation, I have seen both used, but the colon comes out better in $\TeX$.

Georg Cantor was the first; see at least:

By an "aggregate" (Menge) we are to understand any collection into a whole $$M$$ of definite and separate objects $$m$$ of our intuition or our thought. These objects are called the "elements " of $$M$$.

In signs we express this thus :

$$M = \{ m \}.$$

The formal set builder notation:

$$\{ x \mid \varphi(x) \}$$

is an evolution of W&R's Principia Mathematica notation for "abstraction": $$x \in \hat z(\psi z) \equiv \psi x$$.

An early example is in:

The class operator $$\{ x \mid \mathfrak A(x) \}$$ "the class of the $$x$$ such that $$\mathfrak A(x)$$" [footnote : This symbol (used in some newer papers) is here taken, for the sake of easier print, instead of Russell's class symbol $$\hat x \mathfrak A(x)$$, whose adoption was first intended.]

The 2nd French edition of:

On introduira [...] un symbole fonctionnel; dans ce qui suit, nous utiliserons le symbole $$\{ x \mid R \}$$; le terme correspondant ne contient pas $$x$$. C'est de ce terme qu'il s'agira quand on parlera de «l'ensemble des $$x$$ tels que $$R$$». [...] par suite la relation $$R$$ est équivalente à $$x \in \{ x \mid R \}$$.

The notation was not present in the English translation of 1968.

• Thank you! Exactly what I was looking for. And thank you for the links, they will help me answer further questions. – yberman Feb 24 '16 at 15:27