# Thread: fallacy with imaginary numbers

1. ## Re: fallacy with imaginary numbers

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

Originally Posted by grapes
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.

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 .

Originally Posted by grapes
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

According to you
means
if

because you are trying to force the above into

but without understanding that there is no error here:

2. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
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.

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

According to you
means
if

because you are trying to force the above into

but without understanding that there is no error here:

3. ## Re: fallacy with imaginary numbers

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

It is you who end up with

In this way:

4. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
do you deliberately refuse to understand:

It is you who end up with
No, I don't
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. ## Re: fallacy with imaginary numbers

Originally Posted by grapes
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. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
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. ## Re: fallacy with imaginary numbers

Originally Posted by grapes
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. ## Re: fallacy with imaginary numbers

Originally Posted by 7777777
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. ## Re: fallacy with imaginary numbers

Originally Posted by grapes
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. ## Re: fallacy with imaginary numbers

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

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

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