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

Definitions in maths?

  1. Yes

    10 vote(s)
  2. No

    4 vote(s)
  1. Nov 21, 2007 #1
    Are all definitions in maths 'if and only if' statement?

    One book actaully has A=>B as a definition but I should intepret it as A<=>B as the definition?
  2. jcsd
  3. Nov 21, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Think about it for a second. ;)

    For instance, if by "A field is a Galois field if it is of finite cardinality" me meant only that "finite cardinality ==> it's Galois", then it would be without meaning to say that a field is Galois. But our goal is precisely to be able to say "a Galois field" instead of the words "a field of finite cardinality", because it's shorter.
    Last edited: Nov 21, 2007
  4. Nov 21, 2007 #3


    User Avatar
    Gold Member

    oy vei... (-:
  5. Nov 21, 2007 #4


    User Avatar
    Science Advisor

    Yes, every definition says "this" and "that" are the same and so is always an "if and only if" statement. Sometimes people get lazy and don't include the "only if" part, but they should! (I've been guilty of that myself, but I'm notoriously lazy! Often I sit at the computer answering silly questions when I should be workin.)
  6. Nov 22, 2007 #5


    User Avatar
    Gold Member

    Greg doesnt pay enough for the mentorring, well you can go on a strike like the israeli lecturers it won't get you far though.
  7. Nov 22, 2007 #6
    For those who voted no, state your reason.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook