Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Difference between an Equation and an Identity?

  1. Jul 8, 2008 #1
    Can u guys tell me the difference b/w an Equation and an Identity?

    Thx
     
  2. jcsd
  3. Jul 8, 2008 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Re: Identity

    I use the terms quite sloppily myself, but it appears that an identity expresses an equality regardless of the values of any variables. So for example,
    [tex]x(x - 1) = x^2 - x[/tex]
    is an identity, because it is true for any values of x that you plug in. However,
    [tex]x(x - 1) = 0[/tex]
    is an equation, which only holds when specific values for x are plugged in (called the solutions to the equation).
     
  4. Jul 8, 2008 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Re: Identity

    A more interesting identity than one which is just multiplying out a bracket would be something like

    [tex] \sin^2 x + \cos^2 x \equiv 1[/tex]

    Note the three lined symbol which one is supposed to use for identities, rather than the = symbol. Of course, this is something that most of us (me included) would use only if it was really necessary to clarify such a point.
     
  5. Jul 8, 2008 #4
    Re: Identity

    ^ That's odd, I've covered lots of identities and I've never once seen that in any text book (nor during the bajillion trig identities I was forced to prove in highschool.)
     
  6. Jul 8, 2008 #5

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Re: Identity

    Surely it's the first one you prove/meet, and is merely Pythagoras's theorem.
     
  7. Jul 8, 2008 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Identity

    It's not clear whether you are talking about CompuChip's x(x-1)= x2- x or matt grimes' sin2x+ cos2x= 1 but you will find the first in any elementary algebra text and the second in any trigonometry text.
     
  8. Jul 8, 2008 #7
    Re: Identity

    wooosh
     
  9. Jul 8, 2008 #8

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Re: Identity

    I thought he was talking about the 3 line identical equal to symbol.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?