inverse
inverse
1. (converse) of a binary relation R. A derived relation R–1 such that whenever x R y then y R–1 x
where x and y are arbitrary elements of the set to which R applies. The inverse of “greater than” defined on integers is “less than”.
The inverse of a function f: X → Y
(if it exists) is another function, f–1, such that f–1: Y → X
and f(x) = y implies f–1(y) = x
It is not necessary that a function has an inverse function.
Since for each monadic function f a relation R can be introduced such that R = {(x,y) | f(x) = y}
then the inverse relation can be defined as R–1 = {(y,x) | f(x) = y}
and this always exists. When f–1 exists (i.e. R–1 is itself a function) f is said to be invertible and f–1 is the inverse (or converse) function. Then, for all x, f–1(f(x)) = x
To illustrate, if f is a function that maps each wife to her husband and g maps each husband to his wife, then f and g are inverses of one another.
2. See group.
3. of a conditional P→Q. The statement Q→P.
1. (converse) of a binary relation R. A derived relation R–1 such that whenever x R y then y R–1 x
where x and y are arbitrary elements of the set to which R applies. The inverse of “greater than” defined on integers is “less than”.
The inverse of a function f: X → Y
(if it exists) is another function, f–1, such that f–1: Y → X
and f(x) = y implies f–1(y) = x
It is not necessary that a function has an inverse function.
Since for each monadic function f a relation R can be introduced such that R = {(x,y) | f(x) = y}
then the inverse relation can be defined as R–1 = {(y,x) | f(x) = y}
and this always exists. When f–1 exists (i.e. R–1 is itself a function) f is said to be invertible and f–1 is the inverse (or converse) function. Then, for all x, f–1(f(x)) = x
To illustrate, if f is a function that maps each wife to her husband and g maps each husband to his wife, then f and g are inverses of one another.
2. See group.
3. of a conditional P→Q. The statement Q→P.
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inverse