1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Identity Functions

  1. Oct 15, 2008 #1
    From what I was reading, the apparent definition goes as: The Identity Function on E is the function IE from E into E defined by IE(x) = x. Since IE is the set of all ordered pairs (x,x) such that x ϵ E, IE is also called the diagonal subset of E x E.

    If f is a function from E into F, clearly
    1. f o IE = f,
    2. IF o f = f, in which o is a composition operation

    I understood 1., but I'm stuck on understanding on how 2. works. The definition is also confusing me; by how I read it, the identity function is the original function operating on itself...which, as stated, confuses me...any clarifications?
    Last edited: Oct 15, 2008
  2. jcsd
  3. Oct 15, 2008 #2
    What is [itex](I_F\circ f)(x)[/itex] for some element x of E?
  4. Oct 15, 2008 #3
    oh...I sort of understand now...interesting...your presentation suddenly made sense to me...thanks.

    In addition, could I get an example of an identity function for some arbitrary function (so I may further clarify my thoughts)?
  5. Oct 15, 2008 #4
    The identity function does not depend on any arbitrary function. It simply is the function [itex]I_E:E\to E[/itex] which returns its argument unchanged, that is [itex]I_E(x)=x[/itex] for all x in E. For any set E, there is exactly one such function.
  6. Oct 15, 2008 #5
    I see...your answer clarifies things for me...thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook