1. ## empty set

I define S as empty set:
S = {}
Why the Cartesian product S x A (A is not empty set) not defined?
Is
(2) S x S x A
(3) A x S
(4) S x A x S
defined?

2. ## Re: empty set

Originally Posted by policer
I define S as empty set:
S = {}
Why the Cartesian product S x A (A is not empty set) not defined?
Is
(2) S x S x A
(3) A x S
(4) S x A x S
defined?
It may not be defined in your book, but other books define it. Here is how one might define the Cartesian product with the empty set:

Given sets $A,B$, we define $A\times B = \{(a,b)|a\in A, b\in B\}$. If $A=\emptyset$, then there are no candidate choices for $a\in A$, so there are no ordered pairs in $A\times B$, making it the empty set. Similarly if $B=\emptyset$.