What is the differnece between (binary) relation and correspondence?

Question

I'm having hard time understanding the difference between (binary) relation and correspondence.

The definition of binary relation that I know is:
A (binary) relation R between sets X and Y is a subset of the Cartesian product X x Y.

Example with the relation "=": $$X=\{0,1,2,3\}, Y=\{0,1,2,3\}$$ $$R = \{(0,0), (1,1), (2,2), (3,3)\}.$$

The definition of correspondence that I know is:
A correspondence f between X and Y is a triple (X,Y,R) where R is a subset of the Cartesian product X x Y.

Example for correspondence: $$X=\{0,1,2,3\}, Y=\{0,1,2,3\}$$ $$f = (\{0,1,2,3\}, \{0,1,2,3\}, \{(0,0), (1,1), (2,2), (3,3)\})$$

Here is suggested that correspondence is the old term for relation, but I'm still not very convinced, because of the examples that I gave above. Any thoughts?

@WilliamElliot Thank you! I edited the question. R is actually a subset of the X x Y not equal to. I hope that was the thing you meant by "wrong". — Viktor Nonov, May 12 '18 at 18:41
There is little difference. Correspondances package the definition into a triplet while relations rely upon a verbal description which can have the disavantage of loosing sight of X and Y. — William Elliot, May 13 '18 at 03:01
@WiliamElliot I see. by the definitions they seem the same thing, but notated in a different way. If you want, post your comment as an answer, so I can accept it. — Viktor Nonov, May 16 '18 at 16:05

score 0 · Accepted Answer · answered May 17 '18 at 02:04

0

There is little difference. Correspondances package the definition into a triplet while relations rely upon a verbal description which can have the disavantage of loosing sight of X and Y.

answered May 17 '18 at 02:04

William Elliot

17,598

What is the differnece between (binary) relation and correspondence?

1 Answers1