# Thread: relation = "atomic" operation

1. ## relation = "atomic" operation

Is relation is "atomic" operation?

3. ## Re: relation = "atomic" operation

Can I divide the relation concept to other mathematics' concept?

4. ## Re: relation = "atomic" operation

Originally Posted by policer
Can I divide the relation concept to other mathematics' concept?
It is impossible to divide by zero.

5. ## Re: relation = "atomic" operation

Originally Posted by Plato
It is impossible to divide by zero.
Can the set "relation" be in subset? ("divide into another subsets in math)?

6. ## Re: relation = "atomic" operation

Originally Posted by policer
Can the set "relation" be in subset? ("divide into another subsets in math)?

7. ## Re: relation = "atomic" operation

A "relation" between sets X and Y is any subset of X x Y, a set of pairs, (x, y), where x is from set X and y is from set Y. A relation is NOT an "operation" at all so certainly not an "atomic" relation.

8. ## Re: relation = "atomic" operation

Another questions (connected to the subject):
(1)Can I define a relation as a recursive "operation", like: A>1 so also 2A>1, 3A>1 and etc.
So Is there a way as I said to "divide" the relation to other relation that are used in That way?!
(2)Can Relation be reflexive as I said?!

9. ## Re: relation = "atomic" operation

Originally Posted by policer
Another questions (connected to the subject):
(1)Can I define a relation as a recursive "operation", like: A>1 so also 2A>1, 3A>1 and etc.
So Is there a way as I said to "divide" the relation to other relation that are used in That way?!
(2)Can Relation be reflexive as I said?!
1) No, relations are not operations, so they cannot be recursive operations.
2) No. While relations can be reflexive, they are not recursive operations, so they can not be reflexive recursive operations.

Now, that said, it may be possible to define an operator on the set of all relations to itself such that it takes one relation and "divides" it in some way (provided you can make this division well-defined). I would look into representation theory if I were you.

10. ## Re: relation = "atomic" operation

Originally Posted by SlipEternal
1) No, relations are not operations, so they cannot be recursive operations.
2) No. While relations can be reflexive, they are not recursive operations, so they can not be reflexive recursive operations.

Now, that said, it may be possible to define an operator on the set of all relations to itself such that it takes one relation and "divides" it in some way (provided you can make this division well-defined). I would look into representation theory if I were you.
Can someone elaborate the underlined text?
What does he mean?

11. ## Re: relation = "atomic" operation

Did you enter "representation theory" into a search engine?

12. ## Re: relation = "atomic" operation

Originally Posted by SlipEternal
1) No, relations are not operations, so they cannot be recursive operations.
2) No. While relations can be reflexive, they are not recursive operations, so they can not be reflexive recursive operations.

Now, that said, it may be possible to define an operator on the set of all relations to itself such that it takes one relation and "divides" it in some way (provided you can make this division well-defined). I would look into representation theory if I were you.
So, If You classified it by a else word (that is not operation), by which word will it be?!

13. ## Re: relation = "atomic" operation

Originally Posted by policer
So, If You classified it by a else word (that is not operation), by which word will it be?!
I have no idea what idea is in your mind. You have not described what you are trying to do. I do not have the ability to read minds. My suggestion of representation theory was the only idea I had based on the words you used. I can throw out wild guesses if you like.

Here are my guesses. If you are talking about dividing and how it relates to relations, perhaps you are discussing partial orders: Mathworld

If you are talking about equivalence relations, perhaps you mean partitions: Wikipedia

Beyond that, I am out of even wild guesses. I have no idea what you meant in the original post by "atomic".