# Cartesian product.

• Nov 4th 2010, 12:17 PM
Ifailatmaths
Cartesian product.
A={a,b,c,d}
B={y,z}

A x B = {(a,y),(a,z),(b,y),(b,z),(c,y),(c,z),(d,y),(d,z)}

B x A = {(y,a),(y,b),(y,c),(y,d),(z,a),(z,b),(z,c),(z,d)}

I checked the answers and I got A x B wrong but I'm not sure how as I followed the same steps for both.

Supposedly A x B = {(a,y),(b,y),(c,y),(d,y),(a,z),(b,z),(c,z),(d,z)}
• Nov 4th 2010, 12:23 PM
Plato
Quote:

Originally Posted by Ifailatmaths
A={a,b,c,d}
B={y,z}
A x B = {(a,y),(a,z),(b,y),(b,z),(c,y),(c,z),(d,y),(d,z)}
B x A = {(y,a),(y,b),(y,c),(y,d),(z,a),(z,b),(z,c),(z,d)}
I checked the answers and I got A x B wrong but I'm not sure how as I followed the same steps for both.
Supposedly A x B = {(a,y),(b,y),(c,y),(d,y),(a,z),(b,z),(c,z),(d,z)}

Those two answers are identical from a set-theory point of view.
The order in which members are listed makes no difference.
• Nov 4th 2010, 12:32 PM
Ifailatmaths
Quote:

Originally Posted by Plato
Those two answers are identical from a set-theory point of view.
The order in which members are listed makes no difference.

Even for ordered pairs?
• Nov 4th 2010, 12:39 PM
Plato
It is true that in general $(a,x)\not=(x,a)$.

But it is absolutely true that $\{(a,x),(a,y),(b,z)\}=\{(b,z),(a,y),(a,x)\}$

The order in the set makes no difference, only the content of the set.
• Nov 4th 2010, 01:03 PM
MoeBlee
Quote:

Originally Posted by Plato
It is true that in general $(a,x)\not=(x,a)$.

You mean it is not in general true that $(a,x)=(x,a)$.
• Nov 4th 2010, 01:07 PM
Plato
What is the difference?

It is true that $1\not= 2$.
It is not true that $1=2$.
• Nov 4th 2010, 01:26 PM
Ifailatmaths
Quote:

Originally Posted by Plato
It is true that in general $(a,x)\not=(x,a)$.

But it is absolutely true that $\{(a,x),(a,y),(b,z)\}=\{(b,z),(a,y),(a,x)\}$

The order in the set makes no difference, only the content of the set.

Thanks, makes sense.
• Nov 4th 2010, 01:34 PM
MoeBlee
Granted that the word 'generally' or 'in general' is sometimes ambiguous, so that it is context that determines what is meant. And in this context, I think you are well enough understood. However, it is more precise to say "it is not in general true that they are equal".

You say, "It is true in general that they are not equal."

But it is not true in general that they are not equal, since there are instances in which they ARE equal.

I say, "It is not in general true that they are equal", which is true since there are instances in which they are NOT equal.
• Nov 4th 2010, 01:41 PM
Plato
You must a logician. Only logician would worry with that.
• Nov 4th 2010, 01:59 PM
MoeBlee
Quote:

Originally Posted by Plato
You must a logician. Only logician would worry with that.

Or a neurotic. And I am one. ;-)