caretisian product as function

[shahar]

Can Cartesian Product be a function?
I read a book that say things that not clear.
When it can be? Or why the Cartesian Product cannot be a function?

 

[firemath]

My line of thinking:

A B	3	6	9
1	(1,3)	(1,6)	(1,9)
2	(2,3)	(2,6)	(2,9)
3	(3,3)	(3,6)	(3,9)

You're always going to have multiple values for both x and y inputs, therefore making Cartesian products relations, not functions.

But what did the book say exactly?

 

[shahar]

My line of thinking:

A B	3	6	9
1	(1,3)	(1,6)	(1,9)
2	(2,3)	(2,6)	(2,9)
3	(3,3)	(3,6)	(3,9)

You're always going to have multiple values for both x and y inputs, therefore making Cartesian products relations, not functions.

But what did the book say exactly?s

I don't understand.
From the text I quote (from Hebrew):
"[There are many function...
[one of the function is] Cartesian Product that is function only that is in size one and another attributes that we don't mention here. [=in this article]."
What do the author mean?

 

[pka]

I don't understand. From the text I quote (from Hebrew):
"[There are many function...[one of the function is] Cartesian Product that is function only that is in size one and another attributes that we don't mention here. [=in this article]."What do the author mean?

In most axiomatic treatments the definition goes something like this.
The statement that \(f\) is a function means
1) \(f\) is a set of ordered pairs such that
2) each term in the initial set is the first term of some pair in \(f\)
3) no two pairs of \(f\) have the same first term.

 

[Dr.Peterson]

From the text I quote (from Hebrew):
"[There are many function...
[one of the function is] Cartesian Product that is function only that is in size one and another attributes that we don't mention here. [=in this article]."
What do the author mean?

Your translation makes no sense to me, especially lacking context. I could try to guess, but that wouldn't be useful.

Can you paste in the Hebrew, or give us a link, so we can have Google translate it for us, and try to work out what it actually means?

 

[shahar]

O.k. the site is down for a while. But I can tell what I figure out:
You can treat a function as Cartesian Product by making it a machine that get one input and return one output.
When we consider a Cartesian Product as a function one of the sets must be the Y and as Y it needs to be only one variable i.e. "size" one

 

[Dr.Peterson]

O.k. the site is down for a while. But I can tell what I figure out:
You can treat a function as Cartesian Product by making it a machine that get one input and return one output.
When we consider a Cartesian Product as a function one of the sets must be the Y and as Y it needs to be only one variable i.e. "size" one

The trouble is, a function (or, more generally, a relation) is not a Cartesian product, but a SUBSET of a Cartesian product. The entire Cartesian product is NOT a function!