# [FOM] A historical question about notation

Thomas Kucera Thomas.Kucera at umanitoba.ca
Thu Aug 22 00:33:30 EDT 2013

```I'm hesitant to rely on Wikipedia altogether, but re (5):

<http://en.wikipedia.org/wiki/Von_Neumann_universe>

attributes V (for "verum", 'true', 'reality') to Peano, 1889.

There is a brief, interesting account of the earliest (known to the author of the page) uses of the symbols of logic and set theory at

<http://jeff560.tripod.com/set.html>

which attributes cup and cap for union and intersection again to Peano, 1888, much preceding the earliest use of \vee for 'or' (Russell, 1906, 1908) and \wedge for 'and' (Heyting, 1930).

On Aug 19, 2013, at 22:57, <T.Forster at dpmms.cam.ac.uk>
wrote:

> Over lunch today with one of the members of this list, the question of the notation for the empty set came up. I am wondering if listmembers can confirm the following allegations which i find floating around inside my head..
>
> 1   The capital \$\Lambda\$ notation for the empty set (used by Russell and    Quine) is a capital `L' connoting German `leer';
>
> 2   The `v' for disjunction comes from Latin `vel' meaning `or';
>
> 3   `\$\cup\$' for set union derives from vel;
> 4 `\$\cap\$' derives from `\$\cup\$' and `\$\wedge\$' analogously from `\$\vee\$' -
>   turning symbols upside-down connotes duality.
>
> 5   `\$V\$' for the universe is an upside-down `\$\Lambda\$'.
>
> I'm pretty sure about (2) but not at all confident about some of the others.
>
>
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom

```