# Thread: fallacy with imaginary numbers

1. ## 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. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
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.

3. ## Re: fallacy with imaginary numbers

Originally Posted by grapes
Yes
exactly. And they are wrong.

both

and

are true.

4. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
exactly. And they are wrong.

both

and

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

5. ## Re: fallacy with imaginary numbers

Originally Posted by grapes
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 ?

6. ## Re: fallacy with imaginary numbers

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

Tell me exactly:

do you think that
is false ?
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.

7. ## Re: fallacy with imaginary numbers

Originally Posted by grapes

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

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

Originally Posted by grapes
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.

8. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
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

9. ## Re: fallacy with imaginary numbers

Originally Posted by grapes
Yes

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

Originally Posted by grapes
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

10. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
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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