Re: Reflexive And Symmetric

Quote:

Originally Posted by

**Hartlw** The possible relations on {1.2.3} are:

{(1,1), (2,2), (3,3)}

{(1,2), (2,3), (1,3)}

{(2,1) (3,2), (3,1)}

{(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)}

{(1,1), (2,2), (3,3), (2,1), (3,2), (3,1)}

You missed a whole lot of the relations on $\displaystyle \{1,2,3\}$.

There are $\displaystyle 2^9=512$ possible relations.

Any subset of $\displaystyle \{1,2,3\}\times\{1,2,3\}$.

As I said you don't know what a relation is.

Re: Reflexive And Symmetric

Quote:

Originally Posted by

**Plato** You missed a whole lot of the relations on $\displaystyle \{1,2,3\}$.

There are $\displaystyle 2^9=512$ possible relations.

Any subset of $\displaystyle \{1,2,3\}\times\{1,2,3\}$.

As I said you don't know what a relation is.

Not if 1,2,3 are integers, or you accept meaningless definitions which are really not relations. Frankly, I wavered on acceptable subsets. I don't believe they apply for the integers, depending on the definition of "relation," for example {(1,1), (1,2)}, but that's a topic for another discussion. In any event, your post 2 set is not a possible relation for the integers.

Re: Reflexive And Symmetric

Quote:

Originally Posted by

**Hartlw** Not if 1,2,3 are integers, or you accept meaningless definitions which are really not relations. Frankly, I wavered on acceptable subsets. I don't believe they apply for the integers, depending on the definition of "relation," for example {(1,1), (1,2)}, but that's a topic for another discussion. In any event, your post 2 set is not a possible relation for the integers.

If $\displaystyle \mathcal{R}=\{(1,1),~(2,2),~(3,3),~(1,2),~(2,1)\} \subseteq (\mathbb{Z}\times\mathbb{Z})$ then it is a relation in the integers.