What is the cartesian product of Z2 x Z3?

Question

pls. help me with this question.. i am so exhausted with this.. my professor gave us this as our homework but hell!! he didnt even care to discuss what is this!

Answer 1

Z is the set of integers.

Z2 is probably one of two things:
Z^2, the set of all ordered pairs of integers, or
Z_2 (that's Z sub 2), the integers modulo 2.

Let's suppose the 2 is a superscript, like an exponent. Z^2 is the set of all ordered pairs (a,b) such that a and b are integers. Likewise, Z^3 is the set of all ordered triples (c, d, e) such that c, d, and e are integers.

The cartesian product Z^2 x Z^3 asks you to form all possible ordered pairs with first coordinate from Z^2 and second coordinate from Z^3. Officially, that would mean Z^2 x Z^3 is the set of all things of the form ((a,b), (c,d,e)) such that a, b, c, d, and e are integers. It's irritating to have to worry about those interior parentheses, so (depending on your purpose and how formal your prof wants you to keep your answers) you might be able to get away with calling Z^2 x Z^3 the set of all "5-tuples" (a, b, c, d, e) where a, b, c, d, and e are integers. Formalists may object to this.

Given the context, I bet this answer is at least on target. If it turns out your question deals with Z mod 2 and Z mod 3 instead, then please repost and I'll give you a different answer.

Answer 2

If it's the second of the two cases -- the one the first answerer didn't spell out -- then the whole thing has 2x3 = 6 elements.