# Thread: fallacy with imaginary numbers

1. ## Re: fallacy with imaginary numbers

Originally Posted by grapes
Yes, I did, in posts #6 and #8
And I have told why you are wrong:

does not mean +3 = -3

2. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
And I have told why you are wrong:

does not mean +3 = -3
From post #8:
Originally Posted by grapes
At no time did I claim
By the definition of the radical sign, it does not equal -3.

3. ## Re: fallacy with imaginary numbers

Originally Posted by grapes
From post #8:

By the definition of the radical sign, it does not equal -3.
And that is your mistake. You are using a definition. You are defining a true statement as false:

is true

but according to your definition it is false.

You have been given enough evidence proving you wrong, but you are systematically ignoring it all.
You are ignoring the multivaluedness of the square root function, although you said "of course", thus contradicting
yourself. It is perhaps best either to agree or disagree, but not to do both at the same time.

You wrote that "The radical means a single-valued function", but that's only because of your definition. It might be
better to avoid definitions althogether, if they allow you to define anything that you want, even impossibilities like defining true as false.

4. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
And that is your mistake. You are using a definition.
I'm using the same definition as the article that you quoted in the OP.

You can't avoid using definitions. You can choose to use your own, or you can choose to use the ones that everybody else uses.
You are defining a true statement as false:

is true

but according to your definition it is false.

You have been given enough evidence proving you wrong, but you are systematically ignoring it all.
You are ignoring the multivaluedness of the square root function, although you said "of course", thus contradicting
yourself.
Obviously, then, I have not been ignoring it.

ETA: Nobody else is ignoring them either!
It is perhaps best either to agree or disagree, but not to do both at the same time.

You wrote that "The radical means a single-valued function", but that's only because of your definition. It might be
better to avoid definitions althogether, if they allow you to define anything that you want, even impossibilities like defining true as false.
Obviously you cannot avoid definitions altogether.

You should learn what definitions others are using before you criticize them.

5. ## Re: fallacy with imaginary numbers

Originally Posted by grapes
I'm using the same definition as the article that you quoted in the OP.
Both you and the wikipedia article end up with the fallacy -1 = +1
And that is because you both use the same definition.

Originally Posted by grapes
You can't avoid using definitions. You can choose to use your own, or you can choose to use the ones that everybody else uses.
I don't use my own definitions. You don't completely understand the definition you use because you end up with the fallacy. I have told how to solve the fallacy by refuting the wikipedia's denial that both

are true.
Originally Posted by grapes
Obviously, then, I have not been ignoring it.
ETA: Nobody else is ignoring them either!
Obviously you are ignoring multivaluedness of the square root function.

Originally Posted by grapes
Obviously you cannot avoid definitions altogether.You should learn what definitions others are using before you criticize them.
I know the definitions others are using, in fact I know them better then them because how else could I know that what they are doing is wrong. They don't know the solution to the fallacy.

6. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
Both you and the wikipedia article end up with the fallacy -1 = +1
And that is because you both use the same definition.
Read the article again. They present that as a fallacy, and point out the reason for the fallacy.
I don't use my own definitions. You don't completely understand the definition you use because you end up with the fallacy. I have told how to solve the fallacy by refuting the wikipedia's denial that both

are true.
Your definitions are exactly what causes the fallacy. They explain that in the article.

Obviously you are ignoring multivaluedness of the square root function.

I know the definitions others are using, in fact I know them better then them because how else could I know that what they are doing is wrong. They don't know the solution to the fallacy.
ETA: The article explained how to avoid the fallacy. Continuing to use sloppy definitions will eventually result in you falsely concluding something to be true--and you won't be able to recognize it as a mistake.

7. ## Re: fallacy with imaginary numbers

Originally Posted by grapes
Read the article again. They present that as a fallacy, and point out the reason for the fallacy.

Your definitions are exactly what causes the fallacy. They explain that in the article.
I don't have "my definitions", I don't use own definitions. You keep on telling that

means +3 = -3

Originally Posted by grapes
ETA: The article explained how to avoid the fallacy. Continuing to use sloppy definitions will eventually result in you falsely concluding something to be true--and you won't be able to recognize it as a mistake.
That's exactly what you do. You falsely conclude to be true, and you won't be able to
recognize it as a mistake.

The wikipedia article explains that we must suitably constrain the variables in the equality and that in this case the equality does not hold as the numbers are both negative. So let's assume that is right see what happens:

Conclusion: it might help if they first learned to take a square root before starting manipulating the truth. The question is: How can they take a square root of a negative number -9, if they can't even take a square root of a positive number +9?

8. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
I don't have "my definitions", I don't use own definitions.
You use different definitions from everyone else, whosever they are.
You keep on telling that

means +3 = -3
In what post? I couldn't find any post of mine where that appears.
That's exactly what you do. You falsely conclude to be true, and you won't be able to
recognize it as a mistake.

The wikipedia article explains that we must suitably constrain the variables in the equality and that in this case the equality does not hold as the numbers are both negative. So let's assume that is right see what happens:

Conclusion: it might help if they first learned to take a square root before starting manipulating the truth. The question is: How can they take a square root of a negative number -9, if they can't even take a square root of a positive number +9?

9. ## Re: fallacy with imaginary numbers

Originally Posted by grapes
You use different definitions from everyone else, whosever they are.
I don't use my own definitions. You don't understand the definitions you use. Tha's why you constantly get everything wrong.

Originally Posted by grapes
In what post? I couldn't find any post of mine where that appears.
so are you telling

means +3 ≠ -3 ?

10. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
I don't use my own definitions.
You're certainly using a different definition for the radical sign, that much is clear.

You may not like the usual definition, but you're still not using the usual definition.
You don't understand the definitions you use. Tha's why you constantly get everything wrong.

so are you telling

means +3 ≠ -3 ?

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