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Math Help - binary operation

  1. #1
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    binary operation

    What does it mean that to check if S( sub script A) is a group, we need to check that * is a binary operation?

    i thought we only need to check that S( sub script A) satisfy the group axioms of associativity, inverse and identity?

    how do i check that * is a binary operation then?

    thanks!
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    What does it mean that to check if S( sub script A) is a group, we need to check that * is a binary operation?

    i thought we only need to check that S( sub script A) satisfy the group axioms of associativity, inverse and identity?

    how do i check that * is a binary operation then?

    thanks!

    Most authors now define: binary operation on a set A is a map  A\times A\rightarrow A...as simple as that. This means that a bin. op. is a CLOSED operation of two variables from A to itself.
    It can be associative, with inverse and etc., but that's another matter.

    Tonio
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  3. #3
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    does it mean that i need to show that is h, h' are in A then hh' is in A hence it is closed?
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  4. #4
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    Quote Originally Posted by alexandrabel90 View Post
    does it mean that i need to show that is h, h' are in A then hh' is in A hence it is closed?

    No, you don't need to do that IF you're given a BINARY OPERATION AND the definition is what I told you.

    Now, if you're trying to prove something is a bin. Op. then yes: you need to show closedness.

    Tonio
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