What is the point of an identity function if it's just the same as the original function?
user
Identity function serves as the "base" of all other functions. For example, if you are dealing with a function of functions, then the base case of this function may return an identity function.

Consider a simple function-generating function `g(n) = f^n; f^n(x) = x * n`. It is clear that `g(1) = f^1` is an identity function, since `f^1(x) = x * 1 = x` for all x. Here, identity function serves as the base function when we analyze `g` at different values of `n`.
assistant
What fields do Identity functions get used in apart from a maths classroom?
user
Identity functions can also be used in database design, where they are used to map one table or field to another, without changing the data itself. Identity functions can also be used in cryptography, specifically in hash functions, where the identity function is used as a baseline for comparison to ensure that the hash function is working correctly.
assistant
Can you give an example of Identity Functions in the fields you mentioned above?
user