(adsbygoogle = window.adsbygoogle || []).push({}); correct use of "3-tuple"?

(here I use "A" for the universal quantifier, "E" for the existential quantifier, and "e" to indicate elementhood)

My present definition for Transitivity of a relation:

R is a transitive relation on the set B

AxeB AyeB AzeB [((x,y)eR & (y,z)eR)-->(x,z)eR]

which I shorten to:

Ax,y,zeB[((x,y)eR & (y,z)eR)-->(x,z)eR]

But for a certain proof I need Ey rather than Ay, so I'm wondering if I can use a 3-tuple, (x,y,z), in the following way:

A(x,y,z)eB[((x,y)eR & (y,z)eR)-->(x,z)eR]

or would that mean I'd have to be using B^3??

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Correct use of 3-tuple ?

**Physics Forums | Science Articles, Homework Help, Discussion**