[QUOTE=science_man_88;247805]well if each 2-tuple has one relation on it then it would have to be 25. If you say less than,less than or equal to, equal to, greater than or equal to, and greater than , then it's at least 5 but my best guess is 25.[/QUOTE]

No. We'll have to take it a little slower. But that's fine.

[QUOTE=jyb;247807]An excellent question, but one I don't think he's anywhere close to being able to answer.[/QUOTE]

Quite right, as it turns out. At least I called it a "challenge question".

If you don't mind I'll make a multiple-choice question of my own:

The members of the Cartesian product S x S are:
A) ordered pairs
B) members of S
C) S x S
D) sometimes empty
E) A and D
F) B and D

[QUOTE=jyb;247807]An excellent question, but one I don't think he's anywhere close to being able to answer. But we'll see.

As one quick check, sm please answer this multiple-choice question:

The Cartesian product of two sets S and T is:
A) a set
B) a graph
C) a plane
D) a line
E) all of the above
F) none of the above[/QUOTE]

You've beat me once again, I've been able to with my current understanding see it in 3 of the 4 items listed, I could see it as a set of 2-tuples, a plane with #S[TEX]\times[/TEX]#T number of allowable points or, a graph of the plane. But I know that I'm wrong because in a list as such it must be one of the 4 or all or none, my understanding would most point to a plane.

[QUOTE=science_man_88;247815]You've beat me once again, I've been able to with my current understanding see it in 3 of the 4 items listed, I could see it as a set of 2-tuples, a plane with #S[TEX]\times[/TEX]#T number of allowable points or, a graph of the plane. But I know that I'm wrong because in a list as such it must be one of the 4 or all or none, my understanding would most point to a plane.[/QUOTE]

Does post #119 give you a hint? It has an example of a Cartesian product.

[QUOTE=CRGreathouse;247816]Does post #119 give you a hint? It has an example of a Cartesian product.[/QUOTE]

If you mean the word element which would imply a set last i checked. thought you didn't want people giving me hints lol, though you didn't give me it outright.

[QUOTE=science_man_88;247818]If you mean the word element which would imply a set last i checked. thought you didn't want people giving me hints lol, though you didn't give me it outright.[/QUOTE]

So... what are your answers to the multiple-choice questions?

[QUOTE=jyb;247807]The Cartesian product of two sets S and T is:
A) a set
B) a graph
C) a plane
D) a line
E) all of the above
F) none of the above[/QUOTE]

[QUOTE=CRGreathouse;247814]The members of the Cartesian product S x S are:
A) ordered pairs
B) members of S
C) S x S
D) sometimes empty
E) A and D
F) B and D[/QUOTE]

[QUOTE=CRGreathouse;247819]So... what are your answers to the multiple-choice questions?[/QUOTE]

A and E. With a look through #119 I'm positive because a element is in a set, and the Cartesian product in #119 is composed of ordered pairs or 2-tuples.

[QUOTE=science_man_88;247823]A and E. With a look through #119 I'm positive because a element is in a set, and the Cartesian product in #119 is composed of ordered pairs or 2-tuples.[/QUOTE]

It's actually A and A, but no big deal. (The Cartesian product FALSE is empty, but the *elements* of a Cartesian product are never empty -- they're ordered pairs, and no matter what you choose for a and b, (a, b) is not the same as {}.)

So, your turn: Pick a set (call it S) and make a relation on S.

[QUOTE=science_man_88;247823]A and E. With a look through #119 I'm positive because a element is in a set, and the Cartesian product in #119 is composed of ordered pairs or 2-tuples.[/QUOTE]

Ahhh... Man...

You're a dead man walking....

[QUOTE=CRGreathouse;247824]It's actually A and A, but no big deal. (The Cartesian product FALSE is empty, but the *elements* of a Cartesian product are never empty -- they're ordered pairs, and no matter what you choose for a and b, (a, b) is not the same as {}.)

So, your turn: Pick a set (call it S) and make a relation on S.[/QUOTE]

okay what about the Cartesian product of a set S such that S is the empty set, then technically wouldn't you only match up nothing with nothing, but I guess it's not the same.

[QUOTE=chalsall;247825]Ahhh... Man...

You're a dead man walking....[/QUOTE]

name one time I'm not ?