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Thread: fallacy with imaginary numbers

  1. #11
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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by grapes View Post
    No, you end up with that, not me.
    nope. It is you who ends up with the error

    Quote Originally Posted by grapes View Post
    Squaring both sides of an equation is not always a valid algebraic step, for obvious reasons. No need to start with a radical sign, just start with -3 not equal to 3.
    You have started your manipulation. If you start with "-3 not equal to 3" it is not anymore the same as starting with
    Why not?
    Because has two values: is not only equal to +3 but also to -3.

    And let's see now where we end up with this knowledge, taking into account your advice "no need to start with a radical sign":




    You said that squaring both sides of an equation is not always a valid algebraic step. But I have always exposed the mainstream lies and manipulation. And perhaps the real reason for your error is something else. Maybe you should not start with the error .


    Quote Originally Posted by grapes View Post
    You've insisted on that before. That's why you come up with nonsense like
    I don't end up with nonsense. You end up with nonsense:




    does not mean +3 = -3



    Your manipulation says the opposite:
    According to you
    means
    if




    because you are trying to force the above into





    but without understanding that there is no error here:




  2. #12
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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by 7777777 View Post
    nope. It is you who ends up with the error
    That was in your post, not in mine.


    You have started your manipulation. If you start with "-3 not equal to 3" it is not anymore the same as starting with
    Why not?
    Because has two values: is not only equal to +3 but also to -3.

    And let's see now where we end up with this knowledge, taking into account your advice "no need to start with a radical sign":




    You said that squaring both sides of an equation is not always a valid algebraic step. But I have always exposed the mainstream lies and manipulation. And perhaps the real reason for your error is something else. Maybe you should not start with the error .




    I don't end up with nonsense. You end up with nonsense:




    does not mean +3 = -3



    Your manipulation says the opposite:
    According to you
    means
    if




    because you are trying to force the above into





    but without understanding that there is no error here:




  3. #13
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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by grapes View Post
    That was in your post, not in mine.
    do you deliberately refuse to understand:

    It is you who end up with

    because you start with the error


    In this way:




  4. #14
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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by 7777777 View Post
    do you deliberately refuse to understand:

    It is you who end up with
    No, I don't
    because you start with the error
    That is not an error. You seem to be unaware of the definition of the radical sign

    In this way:



    That is illegal algebra. The first line of the three does not imply the second line, algebraically

  5. #15
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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by grapes View Post
    No, I don't

    That is not an error. You seem to be unaware of the definition of the radical sign

    That is illegal algebra. The first line of the three does not imply the second line, algebraically
    The only possibility is that the square root function is



    and, for example


  6. #16
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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by 7777777 View Post
    The only possibility is that the square root function
    By definition, a mathematical function has only one output

    is



    and, for example

    There can't be two results for a single input.

    It's by definition, although there are good reasons for the definition.

  7. #17
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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by grapes View Post
    By definition, a mathematical function has only one output

    There can't be two results for a single input.

    It's by definition, although there are good reasons for the definition.

    square root may be considered a multivalued function

    For example, we may write = 2 = { 2 , − 2 }

    https://en.wikipedia.org/wiki/Multiv...ction#Examples

  8. #18
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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by 7777777 View Post
    square root may be considered a multivalued function

    For example, we may write = 2 = { 2 , − 2 }

    https://en.wikipedia.org/wiki/Multiv...ction#Examples
    Of course.

    But in the article that you criticized in the OP, they were not. Even the article you quote in this post says "In this context, an ordinary function is often called a single-valued function to avoid confusion"

    The radical means a single-valued function, although it can be used in other ways by people, such as yourself. People who use it as a single-valued function are not denying that -2 squared is 4. They're just working with functions (and, in the case in your OP, pointing out the pitfalls of not)

  9. #19
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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by grapes View Post
    People who use it as a single-valued function are not denying that -2 squared is 4
    You still have not told what is wrong with




  10. #20
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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by 7777777 View Post
    You still have not told what is wrong with



    Yes, I did, in posts #6 and #8

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