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Thread: fallacy with imaginary numbers

  1. #1
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    Default fallacy with imaginary numbers

    according to wikipedia there is a fallacy of the following kind:




    https://en.wikipedia.org/wiki/Imagin...gative_numbers

    they are denying that



    are both true.

  2. #2
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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by 7777777 View Post
    according to wikipedia there is a fallacy of the following kind:




    https://en.wikipedia.org/wiki/Imagin...gative_numbers

    they are denying that



    are both true.
    Yes, that is what they mean when they say
    Care must be used when working with imaginary numbers expressed as the principal values of the square roots of negative numbers.
    The radical sign is usually defined as the principal root. So, when you use the radicals, and the rules for multiplying under the radical inappropriately, you can introduce errors. That's what they are pointing out.

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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by grapes View Post
    Yes
    exactly. And they are wrong.


    both

    and


    are true.

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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by 7777777 View Post
    exactly. And they are wrong.


    both

    and


    are true.
    You are using the radical sign differently than most people.

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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by grapes View Post
    You are using the radical sign differently than most people.
    What do you mean? Do you mean that I am wrong?


    Tell me exactly:

    do you think that
    is false ?

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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by 7777777 View Post
    What do you mean? Do you mean that I am wrong?


    Tell me exactly:

    do you think that
    is false ?
    There is another wikipedia page that covers the same thing:
    Every nonnegative real number a has a unique nonnegative square root, called the principal square root, which is denoted by √a, where √ is called the radical sign or radix.
    https://en.m.wikipedia.org/wiki/Square_root

    In other words, √9 means 3, but not -3

    It's just a math symbol. If you want to indicate the negative square root of 9, you indicate it by -√9

    That's just how the symbols are defined.

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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by grapes View Post
    There is another wikipedia page that covers the same thing:

    https://en.m.wikipedia.org/wiki/Square_root

    In other words, √9 means 3, but not -3
    so, you are telling that
    is false

    Quote Originally Posted by grapes View Post
    It's just a math symbol. If you want to indicate the negative square root of 9, you indicate it by -√9

    That's just how the symbols are defined.
    but now you are telling that the negative square root of 9 is -3 ( = -√9)


    You should decide what is , you can't tell that it is both false and true at the same time.

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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by 7777777 View Post
    so, you are telling that
    is false
    Yes



    cannot also equal -3.

    but now you are telling that the negative square root of 9 is -3 ( = -√9)
    Yes.

    If then taking the negative of both sides is



    You should decide what is , you can't tell that it is both false and true at the same time.
    I did not tell that.

    At no time did I claim

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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by grapes View Post
    Yes



    cannot also equal -3.
    alright, then you end up with




    Quote Originally Posted by grapes View Post
    Yes.

    If then taking the negative of both sides is

    I did not tell that.

    At no time did I claim
    You said that the negative square root of 9 is -3.
    And now you are telling that it does not mean

    Whereas I see that it is right to say that
    "the negative square root of 9 is -3" means
    and
    "the positive square root of 9 is +3" means
    Last edited by 7777777; 07-02-2018 at 02:40 PM. Reason: not edited

  10. #10
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    Default Re: fallacy with imaginary numbers

    Quote Originally Posted by 7777777 View Post
    alright, then you end up with


    No, you end up with that, not me.

    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 said that the negative square root of 9 is -3.
    And now you are telling that it does not mean
    It does not mean that. You left out the negative

    Whereas I see that it is right to say that
    "the negative square root of 9 is -3" means
    and
    "the positive square root of 9 is +3" means
    You've insisted on that before. That's why you come up with nonsense like

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