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

Biconditional versus identity

  1. Jun 10, 2008 #1
    Suppose we have a statement A that holds if and only if statement B holds.

    "A if and only if B"

    I'm fairly sure I read before that this does not necessarily mean that A and B are identical: in general, A <--> B does not imply A = B.

    I'm having difficulty determining how A and B could be distinguished from each other - besides, of course, their names.

    I think that a simple, concrete example would clear this up for me; if someone could provide one I'd greatly appreciate it. My sanity's been really wearing thin, lately (just have a look at my other thread; actually, don't)... maybe I should lay off the Red Bulls.
     
  2. jcsd
  3. Jun 10, 2008 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    _Equality_ of logical statements doesn't really make sense. But if you still want an example:

    Let n be an integer, then n is even if and only if n^2 is even.

    It doesn't make sense to say (n is even) equals (n^2 is even), unless you wish to define what you mean by 'equal'. The two statements are equivalent, in the obvious sense.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Biconditional versus identity
  1. Convolution Identity (Replies: 1)

  2. A cool identity (Replies: 9)

  3. Newton's identities (Replies: 0)

  4. Identically zero (Replies: 3)

Loading...