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Thread: Product with undefined term

  1. #1 Product with undefined term 
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    Let c=ab. Assume b is undefined (but bounded). If a=0, is c=0 or is c undefined?


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    KJW
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    Quote Originally Posted by mathman View Post
    Let c=ab. Assume b is undefined (but bounded). If a=0, is c=0 or is c undefined?
    While one could make a reasonable argument for c=0, I'm going with c is undefined.

    EDIT: However, if an inequality that specifies the bound is provided, then b is no longer undefined and it can be proven that c=0.


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    Case of interest f(x)=xsin(1/x). c=f(0).
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    Quote Originally Posted by mathman View Post
    Case of interest f(x)=xsin(1/x). c=f(0).
    I think the goal posts are moved here though, the first equation is algebraic (and b is implicitly some element of a semigroup at least?) while the second is asking something about limits?
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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    Quote Originally Posted by river_rat View Post
    Quote Originally Posted by mathman View Post
    Case of interest f(x)=xsin(1/x). c=f(0).
    I think the goal posts are moved here though, the first equation is algebraic (and b is implicitly some element of a semigroup at least?) while the second is asking something about limits?
    a and b are numbers. In the example a=0 while b=sin(1/0).
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  7. #6  
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    Quote Originally Posted by mathman View Post
    b=sin(1/0).
    That isn't a number though?

    We could consider a linear function space and a functional where we evaluate at x=0, but then sin(1/x) is not an element or the functional is not defined for all elements of the space. Domains matter for questions like this.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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