4
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ I think it was August de Morgan who introduced all these things. $\endgroup$ – Alexandre Eremenko Aug 23 '15 at 20:19
  • $\begingroup$ By the way, I just found out that Grassmann already used the symbol ∪, as cited in Umberto Bottazzini, Va' pensiero, footnote at page 237. $\endgroup$ – mau Jan 26 '16 at 9:10
  • $\begingroup$ I always thought that August de Morgan wrote before Grassmann. $\endgroup$ – Alexandre Eremenko Jan 26 '16 at 21:30
  • $\begingroup$ 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. $\endgroup$ – mau Jan 27 '16 at 8:22
5
$\begingroup$

See Earliest Uses of Symbols of Set Theory and Logic :

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".

$\endgroup$
  • 1
    $\begingroup$ 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... $\endgroup$ – mau Aug 23 '15 at 18:01
  • $\begingroup$ 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 $\endgroup$ – Conifold Aug 25 '15 at 18:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.