Mountain Math Software
home consulting videos book QM FAQ contact

PDF version of this book
next up previous contents
Next: Axiom of union Up: Axioms of Set Theory Previous: Axiom of the empty   Contents

Axiom of unordered pairs

From any two sets $x$ and $y$ one can construct a set that contains both $x$ and $y$. The notation for that set is $\{x,y\}$.

This axiom constructs a new set from any two existing sets.

\begin{displaymath}\forall x \forall y \hspace{.05in} \exists z \hspace{.05in}\forall w \hspace{.1in}w \in z \equiv ( w = x \vee w = y ) \end{displaymath}

This says for every pair of sets $x$ and $y$ there exists a set $w$ that contains $x$ and $y$ and no other members.


Mountain Math Software
home consulting videos book QM FAQ contact
Email comments to: webmaster@mtnmath.com