What Is a Mathematical Relation?

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A mathematical relation is, in general, a relationship between sets of numbers or sets of elements. Find out what makes a mathematical relation into a function with help from a math teacher in this free video on math help and mathematical relations.

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So what is a mathematical relation? Hi, I'm Jimmy Chang, and I've been teaching college mathematics for over nine years, and the phrase "mathematical relation" pretty much implies the word relationship, so let's get into the definition of what it actually is. Now, it is, generally, if you want to talk about in a general sense, it's a relationship between sets -- sets of numbers, sets of elements. It can be between people, it can be words, et cetera. But in terms of, you know, mathematical relations, generally between numbers or variables. Now, typically what happens in a mathematical relation is that every element from one set, generally labeled the X coordinates, is paired with an element in the other set, typically known as the Y coordinates. It doesn't...they aren't necessarily labeled X and Y, but that tends to be the most general relationship that there is. And playing off of that definition: If no two pairs share the same X coordinate, the relation is a function. So no two different pairs can have the same X coordinate, otherwise it would not be a function. It would just be your run-of-the-mill relation. Now, let's give an example as to what the relation can be. Suppose, for example, the X coordinates could have the numbers, let's just say, one, three, and five. And then the Y coordinates will have, let's just say, seven, 10, and let's just say 12.3, as an example. Now, what you want to do is pair off every number from X with a number with a Y. So you can have one, seven, three, 10, and five, 12.3. Now, not the most exciting relation in the world, but you do have a relation, nevertheless. And in this particular case, because no two pairs share the same X coordinate, you have also that of a function. So I'm Jimmy Chang, and that's an example as to what a mathematical relation is.

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