Determining Functions from relations

[frozonecom]

I know that determining functions from relations can be easy.

A relation is a function if every x has a unique y or every first coordinate(domain) of the ordered pair has exactly one second coordinate(range).

What I don't know is if the repetition of an ordered pair affect the set at all. Will it be considered only as a relation? Or perhaps still a function? Here is an example.

{(6,2) , (4,3) , (5,3) , (6,2) , (7,3) , (2,9)}

Notice the repetition of the ordered pair (6,2). So, will it be considered as a function?

 

[micromass]

Hi frozonecom!

Sets are uniquely determined by it's elements regardless of the order of the elements (that is, the set {0,1} is equal to the set {1,0}) and regardless of the multiplicity of the elements. The latter means that sets such as {0,1,1,1,1,1}, where 1 appears 5 times, are actually equal to {0,1}.

A more rigourous argument why {0,1}={0,1,1,1,1,1} is because every element in the left-hand side is in the right-hand side, and conversely.

Thus, in your example, the set {(6,2) , (4,3) , (5,3) , (6,2) , (7,3) , (2,9)} is actually equal to {(6,2) , (4,3) , (5,3) , (7,3) , (2,9)}, and it is thus a function.

An advice is to never write sets such that elements occur more than once. So never write {0,1,1}, but write {0,1}. This eliminated a lot of confusion...

 

[frozonecom]

Thanks for the quick reply! I was having confusion about the matter. Really appreciate your help! Thanks! :)