INVERSE RELATION Meaning and
Definition
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Inverse relation is a mathematical concept that refers to a relationship between two sets of elements where each element of one set corresponds to exactly one element of the other set, and vice versa. In other words, an inverse relation is a pairing between elements from two sets, such that if one element from the first set is chosen, then its corresponding element from the second set can be uniquely identified.
In an inverse relation, the elements in one set are said to be the "inputs" while the elements in the other set are the "outputs." For example, let A and B be two sets, if an element a from set A corresponds to an element b from set B, then it can be said that a and b have an inverse relation.
To further illustrate, the inverse relation of a function is a relation that pairs each output value with its corresponding input value. If (x, y) is a point on a given function, then (y, x) is a point on its inverse relation.
Inverse relations can be represented graphically as well, typically by exchanging the x and y coordinates in a graph. The graph of an inverse relation is simply the reflection of the original relation over the line y = x, resulting in a symmetrical mirror image.
In summary, an inverse relation is a mathematical relationship between two sets of elements, where each element in one set uniquely corresponds to an element in the other set, and they maintain a symmetrical pairing.
Etymology of INVERSE RELATION
The word "inverse" comes from the Latin word "inversus", which means "turned upside down" or "inverted". It is derived from the verb "invertere", which combines the prefix "in-" meaning "in, into" and the verb "vertere" meaning "to turn".
The word "relation" has Latin roots as well, from the noun "relatio" which means "a bringing back" or "a report". It is derived from the verb "referre", which combines the prefix "re-" meaning "back" and the verb "ferre" meaning "to carry".
Therefore, when combined, "inverse relation" refers to a relationship or connection that is turned upside down or reversed, implying a change in the direction or order of things.
