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The definition of a Relation is a set of ordered pairs

So are Relations just sets of ordered pairs ? I mean if there is a set of ordered pairs that carries no definite relation between it's pairs [and I mean by definite relation, relations like (=), (<) or any type of definite relation] can also be considered a relation ?

So is it just set of pairs ?

Mans
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1 Answers1

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A set of ordered pairs is one way to formalize a relation (specifically, it formalizes the notion of relation in the language of set theory). There are other ways; remember that formalizations, while useful, are not themselves the concepts they represent - they are merely tools for better-understanding those concepts.

user3716267
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    but I've read in a paper ''that it doesn't matter how the relation is defined only what matters is the elements that is related'' so according to this paper relation is just ordered pairs and it doesn't matter if there is a definite relation between pairs so if the pairs carry a definite relation between them or they doesn't so they still represent a relation. – Mans Apr 23 '22 at 22:16
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    and we can create an ordered pairs that we can't distinguish any relation between them and we say that they define a relation because we ruled in our definition that the relation is just ordered pairs example: I can define a relation R={(1,a),(2,c),(pi,50)} so you can't distinguish any relation between pairs but still they represent a relation – Mans Apr 23 '22 at 22:32
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    ''It is important to realize that the objects x and f(x) which appear in the ordered pairs (x, f (x)) of a function need not be numbers but may be arbitrary abjects of any kind. Occasionally we shall use this degree of generality'' from apostol calculus book – Mans Apr 23 '22 at 22:50