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Thread: Simple, strange, annoying...

  1. #1 Simple, strange, annoying... 
    Forum Freshman jmd_dk's Avatar
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    Consider the equation


    What is x? Well:









    I'm a physicist, not a mathematician. In physics, we always check our result; is it reasonable? Let's do it here:



    Well, here's the problem... Is 2 truly a solution to the equation? If we take a look at the limit of the left-hand expression as , it supports that x is a solution:


    When we take this limit, the expression is determined to be 4; hence 2 is a solution to the equation at the top. As we have seen though, isn't working very well in practice. So, the big questions:

    Is it mathematically correct to say that 2 is a solution to the equation?
    - If the answer is yes, doesn't it create a problem that the left-hand side turns out to be , when we are calculation something that can be expressed by this equation?


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  3. #2 Re: Simple, strange, annoying... 
    . DrRocket's Avatar
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    Quote Originally Posted by jmd_dk
    Consider the equation


    What is x? Well:









    I'm a physicist, not a mathematician. In physics, we always check our result; is it reasonable? Let's do it here:



    Well, here's the problem... Is 2 truly a solution to the equation? If we take a look at the limit of the left-hand expression as , it supports that x is a solution:


    When we take this limit, the expression is determined to be 4; hence 2 is a solution to the equation at the top. As we have seen though, isn't working very well in practice. So, the big questions:

    Is it mathematically correct to say that 2 is a solution to the equation?
    - If the answer is yes, doesn't it create a problem that the left-hand side turns out to be , when we are calculation something that can be expressed by this equation?
    No, 2 is not a solution, because the original expression is not defined at 2. But the lack of definition at 2 can be "fixed" if one redefines things a bit.

    You might look at the problem this way



    This last expression clearly extends to and in that case the equation becomes . Now this is trivially solved and the solution is , but of course in order to reach this conclusion we had to extend the definition of the original function to the case


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  4. #3 Re: Simple, strange, annoying... 
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    Quote Originally Posted by jmd_dk
    I'm a physicist, not a mathematician. In physics, we always check our result; is it reasonable? Let's do it here:
    The implication being that mathematicians don't know how to check their work
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  5. #4 Re: Simple, strange, annoying... 
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    Quote Originally Posted by salsaonline
    Quote Originally Posted by jmd_dk
    I'm a physicist, not a mathematician. In physics, we always check our result; is it reasonable? Let's do it here:
    The implication being that mathematicians don't know how to check their work
    The implication being that he is not a mathematician and does not know, obviously.
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