[QUOTE=science_man_88;247688]each box is a representation of the # of moves specific chess pieces can do from each square I relate this to my example of a chess board being a Cartesian product with each square's name being represented by a 2-tuple.[/QUOTE]

First of all, Cartesian products are not a subject of number theory. They are a very basic part of set theory, which underlies all of mathematics. By learning about them, you haven't even started to get to number theory yet. That's why they're in the "preliminaries" section.

Second, relating your counting of chess moves to Cartesian products by pointing out that you can label the squares using the product of your two sets would be like me noticing that the street outside is named 68th and claiming that a list of street names in my city could be helpful for understanding mathematics ("I relate this to my example of a street that has a number in its name").

Why don't you follow Paul's advice and get back to the subject that started this thread? I think it has been adequately demonstrated that there are many people who would be happy to help you learn. But that good will will quickly evaporate if you can't stay on topic, recognize your own limitations, make decent attempts at the suggested problems, and stay on topic.

Since it was a subject that was causing you trouble, have you given any further thought to relations? Do you feel that you can come up with some examples of your own? Can you now understand the formal definition?

[QUOTE=jyb;247741]First of all, Cartesian products are not a subject of number theory. They are a very basic part of set theory, which underlies all of mathematics. By learning about them, you haven't even started to get to number theory yet. That's why they're in the "preliminaries" section.

Second, relating your counting of chess moves to Cartesian products by pointing out that you can label the squares using the product of your two sets would be like me noticing that the street outside is named 68th and claiming that a list of street names in my city could be helpful for understanding mathematics ("I relate this to my example of a street that has a number in its name").

Why don't you follow Paul's advice and get back to the subject that started this thread? I think it has been adequately demonstrated that there are many people who would be happy to help you learn. But that good will will quickly evaporate if you can't stay on topic, recognize your own limitations, make decent attempts at the suggested problems, and stay on topic.

Since it was a subject that was causing you trouble, have you given any further thought to relations? Do you feel that you can come up with some examples of your own? Can you now understand the formal definition?[/QUOTE]

I doubt I can understand it all I know some example but I have no idea about relations obviously I kinda get about the a1 being false in CRG's post but I don't see what I could do with it, to prove equivalence relations etc.

[QUOTE=science_man_88;247750]I doubt I can understand it all I know some example but I have no idea about relations obviously I kinda get about the a1 being false in CRG's post but I don't see what I could do with it, to prove equivalence relations etc.[/QUOTE]

It sounds like you were trying to move too fast. So let's back up. Forget for a moment about what makes a relation an equivalence relation. Try answering the questions I just posed. In particular, I want to know if you feel comfortable with the formal definition of a relation yet. That's not vital right away, but it would certainly simplify the subsequent discussion.

[QUOTE=jyb;247757]It sounds like you were trying to move too fast. So let's back up. Forget for a moment about what makes a relation an equivalence relation. Try answering the questions I just posed. In particular, I want to know if you feel comfortable with the formal definition of a relation yet. That's not vital right away, but it would certainly simplify the subsequent discussion.[/QUOTE]

my understanding from what I read is that a binary relation is a relation in a

2-tuple in a subset of the Cartesian product of A and B, if this Cartesian product is the x and y plane I'd see it as a relation of the points that make up a subset like a line. I know this is probably wrong, as are most of my guesses.

[QUOTE=science_man_88;247759]my understanding from what I read is that a binary relation is a relation in a

2-tuple in a subset of the Cartesian product of A and B, if this Cartesian product is the x and y plane I'd see it as a relation of the points that make up a subset like a line. I know this is probably wrong, as are most of my guesses.[/QUOTE]

Well, it's not so much wrong as it is non-sensical. What does "a relation in a 2-tuple in a subset" mean? Or "a relation of the points that make up a subset"? Saying things like that makes it pretty clear that you're not really getting it yet.

But don't despair! You need more practice and you need to put in some hard work thinking about this. You shouldn't expect it all to come easily. But you can still get it if you try.

For starters, let's look at the definition you cited at the beginning of this thread. That was for a "relation on a set S". In such a case, there is only one set (S) being considered, so talking about the Cartesian product of A and B makes no sense. Instead, you must think about the Cartesian product of S with itself. I.e. S x S.*

As an example, let S be the integers 1 through 5. Do you see what S x S looks like?

* I assume you realize that the choice of letters doesn't matter. We could just as easily have talked about a relation on A, in which case we would be considering the Cartesian product A x A.

[QUOTE=jyb;247762]Well, it's not so much wrong as it is non-sensical. What does "a relation in a 2-tuple in a subset" mean? Or "a relation of the points that make up a subset"? Saying things like that makes it pretty clear that you're not really getting it yet.

But don't despair! You need more practice and you need to put in some hard work thinking about this. You shouldn't expect it all to come easily. But you can still get it if you try.

For starters, let's look at the definition you cited at the beginning of this thread. That was for a "relation on a set S". In such a case, there is only one set (S) being considered, so talking about the Cartesian product of A and B makes no sense. Instead, you must think about the Cartesian product of S with itself. I.e. S x S.*

As an example, let S be the integers 1 through 5. Do you see what S x S looks like?

* I assume you realize that the choice of letters doesn't matter. We could just as easily have talked about a relation on A, in which case we would be considering the Cartesian product A x A.[/QUOTE]

I'd imagine it looks somewhat like a graph for a line where 1,2,3,4,5 are the only accepted values.

[QUOTE=science_man_88;247771]I'd imagine it looks somewhat like a graph for a line where 1,2,3,4,5 are the only accepted values.[/QUOTE]

I don't know what you mean by that. What does it mean for a line to have "accepted values"? And what would something that is "somewhat like a graph for a line" look like? Please try to be precise in your wording so we don't have to spend time trying to figure out what you might have meant. Ask yourself this: if someone else had written what you wrote, do you think you would know what they meant?

In any case, when I asked you what S x S "looked like", I probably made you think about pictures and graphs, which was not at all my intention. What I really meant was this: can you describe S x S in a succinct way? Hint: Keep in mind what the Cartesian product of {a,b,c,d,e,f,g,h} x {1,2,3,4,5,6,7,8} was.

[QUOTE=jyb;247775]I don't know what you mean by that. What does it mean for a line to have "accepted values"? And what would something that is "somewhat like a graph for a line" look like? Please try to be precise in your wording so we don't have to spend time trying to figure out what you might have meant. Ask yourself this: if someone else had written what you wrote, do you think you would know what they meant?

In any case, when I asked you what S x S "looked like", I probably made you think about pictures and graphs, which was not at all my intention. What I really meant was this: can you describe S x S in a succinct way? Hint: Keep in mind what the Cartesian product of {a,b,c,d,e,f,g,h} x {1,2,3,4,5,6,7,8} was.[/QUOTE]

something like the graph in the attached file but without the line and only the integers are allowed values.

[QUOTE=jyb;247775]What I really meant was this:[/QUOTE]

As a good friend of mine once advise me: be responsible for the listening into which you are speaking.

Even if the listeners are ignorant....

[QUOTE=science_man_88;247777]something like the graph in the attached file but without the line and only the integers are allowed values.[/QUOTE]

Care to ZIP your data using a format which we simple humans can understand? (As you did just earlier today.)

Gosh... And I though you were sincere about your PM'ed tear-jerking family story....

[QUOTE=chalsall;247779]Care to ZIP your data using a format which we simple humans can understand? (As you did just earlier today.)

Gosh... And I though you were sincere about your PM'ed tear-jerking family story....[/QUOTE]

what I sent you was correct about my family.

okay what format ? I have 7 zip lol it seems to have a million different ways.

the new one I just replaced it with good ? that's using add to archive.