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Thread: functions = groups

  1. #1
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    functions = groups

    Can I define some functions as groups ecxept continuous function? Can somebody give me other examples of function that are group?
    Thank you.
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  2. #2
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    Re: functions = groups

    Quote Originally Posted by policer View Post
    Can I define some functions as groups ecxept continuous function? Can somebody give me other examples of function that are group?
    Thank you.
    Functions are never groups. A group is a set and a binary operator. A function may be a binary operator, but it is not a set. A function may be an action on a group, but it is still not a group by itself.
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  3. #3
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    Re: functions = groups

    A set of functions, with a given operation, may be a group. For example, the set of all polynomials, of degree n or less, for any positive integer n, with addition as operation is a group. The "identity" is the constant polynomial, p(x)= 0 for all x. The "additive inverse" of the polynomial $a_nx^n+ a_{n-1}x^{n-1}+ \cdot\cdot\cdot+ a_1x+ a_0$ is $-a_nx^n- a_{n-1}x^{n-1}- \cdot\cdot\cdot- a_1x- a_0$.

    The set of all invertible functions is a group with "composition" as operation.
    Last edited by HallsofIvy; Dec 19th 2017 at 09:03 AM.
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  4. #4
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    Re: functions = groups

    policer, it would help if you would state what definitions of "function" and "group" you are using.
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  5. #5
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    Re: functions = groups

    Quote Originally Posted by HallsofIvy View Post
    policer, it would help if you would state what definitions of "function" and "group" you are using.
    This is nothing more than a spammer reviving a dead thread. The OP has not posted in two weeks. The spammer just wanted to advertise a different website.
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