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The concept of inverses is strongly related to that of "identity". A mathematical object, when combined with its inverse, will produce the relevant identity. In the examples above zero is the identity for addition, and the function which leaves things unchanged is called the identity function.
The concept of inverses is strongly related to that of "identity". A mathematical object, when combined with its inverse, will produce the relevant identity. In the examples above zero is the identity for addition, and the function which leaves things unchanged is called the identity function.
==Examples==
*The additive inverse of a number is the number which when added to the original number makes 0, the additive identity. The inverse of positive numbers is simply their negative, of negative numbers similarly their corresponding positive.
*The additive inverse of a number is the number which when added to the original number makes 0, the additive identity. The inverse of positive numbers is simply their negative, of negative numbers similarly their corresponding positive.
*The inverse of a function is a function that reverses the action of the original function. Not all functions are invertible; for example the square of both -3 and 3 is 9, so if we were to reverse this, by square rooting, we would have to decide whether to return from 9 back to the 3 or the -3. This problem can be solved by limiting the domain of the original function (in our example to non-negative numbers). Composing a function with its inverse yields the identity function.
*The inverse of a function is a function that reverses the action of the original function. Not all functions are invertible; for example the square of both -3 and 3 is 9, so if we were to reverse this, by square rooting, we would have to decide whether to return from 9 back to the 3 or the -3. This problem can be solved by limiting the domain of the original function (in our example to non-negative numbers). Composing a function with its inverse yields the identity function.
[[category:mathematics]]
[[Category:Mathematics]]