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Math Help - n+w is w, bt w+n is not w. Why?

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    n+w is w, bt w+n is not w. Why?

    cannot comprehend this from my text book. How to understand this?

    Consider the order types w and n. It is easy to see that n+w=w. In fact, if finitely many terms are written to the left of the sequence 1,2,...,k,..., we again get a set of the same type(why?). On the other hand, the order type w + n, i.e., the order type of the set {1,2,...,k,...,a1,a2,...,an} is obviously(?) not equal to w.
    Last edited by ninano1205; February 17th 2009 at 01:02 PM. Reason: need to be more specific..
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    Like a stone-audioslave ADARSH's Avatar
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    Why: Because the textbooks can be wrong.

    If
    n+w = w
    Then it is a MUST that
    w+n =w
    Last edited by ADARSH; February 17th 2009 at 10:45 AM.
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    Quote Originally Posted by ADARSH View Post
    Why: Because the textbooks can be wrong.
    If n+w = w Then it must be true that w+n =w
    Are you sure about that?
    What if this is a noncommutative operation symbolized by +?
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by Plato View Post
    Are you sure about that?
    What if this is a noncommutative operation symbolized by +?
    I accept it
    EDIT: What Plato says is correct, it could be any other non-commutative function or rather it should be

    non-commutative operation
    The result of operation depends on the order
    eg; Substraction

     <br />
a-b \ne b-a<br />

    untill  a = b
    Last edited by ADARSH; February 17th 2009 at 11:02 AM.
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  5. #5
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    Quote Originally Posted by ninano1205 View Post
    cannot comprehend this from my text book. How to understand this?
    We need more information. What are n and m? Are they numbers? Is "+" the usual addition of numbers or is it defined differently?
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  6. #6
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    Quote Originally Posted by Plato View Post
    Are you sure about that?
    What if this is a noncommutative operation symbolized by +?
    Even for a noncommutative operation, n+ 0= 0+ n where "0" represents the operation identity. In order for n+ m= m with n NOT the identity, the operation must be very odd!
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