# When was the term “union” first used?

I found out that the symbol for union, ∪, was created in 1895 by Giuseppe Peano in his Formulario Mathematico but of course the use of the word "union" in mathematics was older. Do you have a source for the earliest occurrence?

• I think it was August de Morgan who introduced all these things. – Alexandre Eremenko Aug 23 '15 at 20:19
• By the way, I just found out that Grassmann already used the symbol ∪, as cited in Umberto Bottazzini, Va' pensiero, footnote at page 237. – mau Jan 26 '16 at 9:10
• I always thought that August de Morgan wrote before Grassmann. – Alexandre Eremenko Jan 26 '16 at 21:30
• De Morgan possibly wrote before Grassman, but in the comment (as opposed to the post, this is why it's a comment) I talked about the symbol for union. – mau Jan 27 '16 at 8:22

Intersection and union. The symbols $\cap$ and $\cup$ were used by Giuseppe Peano (1858-1932) for intersection and union in 1888 in Calcolo geometrico secondo l'Ausdehnungslehre di H.Grassmann (Cajori vol. 2, page 298).

See page 2 :

1. Colla scrittura $A \cup B \cup C \cup \ldots$ intenderemo la minima classe che contiene le classi $A, B, C,\ldots$, ossia la classe formata dagli enti che sono o $A$ o $B$ o $C$, ecc. Il segno $\cup$ si leggerà o; l'operazione indicata col segno $\cup$ chiamasi in logica disgiunzione; noi la diremo anche addizione logica; le classi $A, B,\ldots$ si diranno i termini della somma $A \cup B \cup \ldots$ [With the symbol $A \cup B \cup C \cup \ldots$ we mean the least class containing the classes $A, B, C,\ldots$, i.e. the class formed by the entities that are either $A$ or $B$ or $C$, etc. The symbol $\cup$ will be read "or"; the operation denoted by the symbol $\cup$ is named in logic disjunction; we will call it also logical sum; the classes $A, B,\ldots$ will be called terms of the sum $A \cup B \cup \ldots$.]

For the term, we have to search : W&R's Principia is still under Peano's influence; see page 27 : "Similarly the logical sum of two classes $\alpha$ and $\beta$ ..."

Some early occurrences are :

• Felix Hausdorff, Set theory (Engl.transl (1957) of the 3rd German ed. 1937), page 18 : "If $A, B$, are two sets, then by their sum, or union ..." [but it is necessary to check on the earlier German editions.]

• Waclaw Sierpinski, Algèbre des ensembles (1951), page 62 : "somme (ou réunion) des ensembles".

• My fault - I meant the first use of the word "union". I edited my question. However, since Peano wrote about "disjunction", maybe the word "union" came later... – mau Aug 23 '15 at 18:01
• I also suspect Hausdorff's 1914 Foundations of Set Theory or one of earlier papers. From Boole to Zermelo they were saying "sums", and there was a trend of mixing sets and classes. According to Kanamori, Hausdorff was first to treat sets purely extensionally, so union made more sense. math.bu.edu/people/aki/8.pdf – Conifold Aug 25 '15 at 18:01