We know that cartesian product of two sets and is:
and
the integer quotient obtained when is divided by
the integer remainder obtained when is divided by
I'm reading a Discrete math book and I am on Functions chapter. It has a line in it that says:
" and are really functions defined on Cartesian products of integers."
For what reason is this statement true? I know it's true but I've no idea why.
I don't see the connection between Cartesian product and the , functions.
Can anyone kindly tell me when I use and functions how is that they are really functions on Cartesian products of integers?
Thank you for your answer. I didn't give the name of book. Sorry about that.
I'm reading Susanna S. Epp's Discrete Mathematics with Applications(Second Edition).
So if and
For and function what do you assign here?
There are elements of . How do you calculate and here?
Can you kindly explain on asssigning an integer to ? Sorry for not understanding.
Sorry for reopening this thread. I thought I understood the problem. Sorry for jumping to conclusion so quickly.
@Plato:
Can you kindly elaborate on what you said about "assign pairs of integers to an integer" comment?
I no longer have a copy of Epp's book. As I recall, wrote a positive review to the publisher. Because I have a positive impression of that text some of wording you posted worries me.
For the mod operator, it is clear that one could apply that operator to any pair integers and the output is an integer.
Examples from MathCad: .
But on the other hand, there is no similar understanding for what could mean. Clearly it is not true that any integer divides every integer. So how exactly does she define the operator?
If that is important to you may I suggest Discrete Mathematics for Teachers
I did an Eisenhower Institute as a test site for that text.
IMO it was a huge success with the in service high school teachers.