What is the unique root of y=sqrt(x)+2?

R.H.

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On 2/15/25 3:45 PM, Richard Hachel wrote:

What is the unique root of y=sqrt(x)+2?

R.H.

4 * i^4

Of course the problem is that if you want the power function for
non-integers to be a simple function, then your number space needs to
keep track of extra rotations around the origin.

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Le 16/02/2025 à 02:42, Richard Damon a écrit :

4 * i^4

Absolutely.

J'avais toujours dit que les Richard étaient des êtres exceptionnels.

Nota bene:

4 * i^4 = -4

In Cartesian representation, point A, root of the equation
f(x)=sqrt(x)+2, is located at A (-4,0) in standard coordinates, and at
A(4i,0) in imaginary coordinates.

R.H.

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On 2/16/25 9:27 AM, Richard Hachel wrote:

Le 16/02/2025 à 02:42, Richard Damon a écrit :

4 * i^4

Absolutely.

J'avais toujours dit que les Richard étaient des êtres exceptionnels.

Nota bene:
4 * i^4 = -4

No, i^4 - 1, since i^2 = -1, by definition.

The problem is that when we collapse to a simple Cartesian system, we
lose the wraps, so non-integer powers become somewhat indeterminate and multiplicative. The "angle" of a number is only known to within a
modulus of 2xPi (or 360 degrees) and thus the square root of any number
has two values. When in just the real domain, we can limit to the
principle limb, but once we allow for complex numbers, we lose that option.

In Cartesian representation, point A, root of the equation
f(x)=sqrt(x)+2, is located at A (-4,0) in standard coordinates, and at A(4i,0) in imaginary coordinates.

R.H.

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Le 16/02/2025 à 19:39, Richard Damon a écrit :

On 2/16/25 9:27 AM, Richard Hachel wrote:

Le 16/02/2025 à 02:42, Richard Damon a écrit :

4 * i^4

Absolutely.

J'avais toujours dit que les Richard étaient des êtres exceptionnels.

Nota bene:
4 * i^4 = -4

No, i^4 - 1, since i^2 = -1, by definition.

When definitions are incorrect, the definitions should be ignored.

Dire que i²=-1, cela est correct, et cela fait partie de la définition, même si cette définition est scandaleuse.

Il est tout à fait anormal, et tout à fait scandaleux, que les mathématiciens n'aient pas expliqué
ce qui allait advenir du système qu'ils imposaient et qui est le système
des imaginaires et des complexes.

C'est un scandale mathématique qui a aveuglé tout le monde.

Et on a dit i²=-1.

Certes, dans ce système, c'est vrai.

Et donc [-4(-)(+)sqrt(16-20)]/2a ----> -2(-)(+)i

Certes.

Mais la bourde n'est pas là. Jusqu'ici, il n'y a PAS de bourde.

La bourde va apparaitre quand on va poser, pour des équation du
quatrième degré, par exemple,
(i²)=-1 DONC (i²)(i²)=1

Ici, inconsciemment, on fait une bourde monumentale.

On applique à l'imaginaire une opération propre aux réels.

Dans le réel si n=1 alors (n²)(n²)=1.

Certes. Je ne nie pas cela.

Mais je nie que dans l'imaginaire, où tout est en miroir, (i²)(i²)=1.

C'est faux. Dans l'imaginaire, i°=-1, i^1=-1 (c'est à dire i=-1),
etc...

Et on va avoir (i²)²=-1.

La même invariabilité qui existe pour 1 (qui reste 1 quoi qu'on fasse)
va exister en miroir
des lois mathématiques de l'autre côté.

Toujours, toujours, toujours et auras 1^x=1 et toujours, toujours,
toujours, tu auras i^x=-1.

C'est la base même de la logique et de la beauté mathématique.

Se limier à i²=-1 comme pendant des siècles, c'est moche.

Il fallait dire POURQUOI, et surtout ce qui adviendrait pas changement de puissance x.

Cela n'a jamais été fait.

R.H.

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On 2/16/2025 4:34 PM, FromTheRafters wrote:

Chris M. Thomasson explained on 2/16/2025 :

On 2/16/2025 11:04 AM, Richard Hachel wrote:

Le 16/02/2025 à 19:39, Richard Damon a écrit :

On 2/16/25 9:27 AM, Richard Hachel wrote:

Le 16/02/2025 à 02:42, Richard Damon a écrit :

4 * i^4

Absolutely.

J'avais toujours dit que les Richard étaient des êtres exceptionnels. >>>>>
Nota bene:
4 * i^4 = -4

No, i^4 - 1, since i^2 = -1, by definition.

When definitions are incorrect, the definitions should be ignored.

Go ahead an ignore the complex numbers. Why should we care?c

[...]

Plus sqrt(-one)

𝑖 see what you did there.

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Le 16/02/2025 à 21:50, "Chris M. Thomasson" a écrit :

On 2/16/2025 11:04 AM, Richard Hachel wrote:

Le 16/02/2025 à 19:39, Richard Damon a écrit :

On 2/16/25 9:27 AM, Richard Hachel wrote:

Le 16/02/2025 à 02:42, Richard Damon a écrit :

4 * i^4

Absolutely.

J'avais toujours dit que les Richard étaient des êtres exceptionnels. >>>>
Nota bene:
4 * i^4 = -4

No, i^4 - 1, since i^2 = -1, by definition.

When definitions are incorrect, the definitions should be ignored.

Go ahead an ignore the complex numbers. Why should we care?

[...]

That's not what I said.
I spoke of "definitions" and not of "matter".
I was saying that false and lame definitions should be ignored, and
replaced by truer, clearer, more beautiful definitions.
It's not that complex numbers should not be studied, it's that if we study them, we must study them correctly and with the right definitions.
Once that's done, everything that remains can be thrown in the trash.
Let's take the very definition of the entity i. Mathematicians propose definitions so ugly, even false, that it will make future generations
laugh.
It is these falsehoods and distortions that deserve to disappear.
I said the same thing about special relativity, and I am then considered
in several ways (a madman who denies everything, a crank who destroys what
is good).
All this is not very serious on the part of men.
N.B. Artificial intelligence can be used to straighten out definitions. I
have already heard it say wonderful things as long as we enter the right
data.

R.H.

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Le 17/02/2025 à 02:08, Richard Damon a écrit :

On 2/16/25 6:11 PM, Richard Hachel wrote:

Le 16/02/2025 à 21:50, "Chris M. Thomasson" a écrit :

On 2/16/2025 11:04 AM, Richard Hachel wrote:

Le 16/02/2025 à 19:39, Richard Damon a écrit :

On 2/16/25 9:27 AM, Richard Hachel wrote:

Le 16/02/2025 à 02:42, Richard Damon a écrit :

4 * i^4

Absolutely.

J'avais toujours dit que les Richard étaient des êtres exceptionnels. >>>>>>
Nota bene:
4 * i^4 = -4

No, i^4 - 1, since i^2 = -1, by definition.

When definitions are incorrect, the definitions should be ignored.

Go ahead an ignore the complex numbers. Why should we care?

[...]

That's not what I said.
I spoke of "definitions" and not of "matter".
I was saying that false and lame definitions should be ignored, and
replaced by truer, clearer, more beautiful definitions.
It's not that complex numbers should not be studied, it's that if we
study them, we must study them correctly and with the right definitions.
Once that's done, everything that remains can be thrown in the trash.
Let's take the very definition of the entity i. Mathematicians propose
definitions so ugly, even false, that it will make future generations
laugh.
It is these falsehoods and distortions that deserve to disappear.
I said the same thing about special relativity, and I am then considered
in several ways (a madman who denies everything, a crank who destroys
what is good).
All this is not very serious on the part of men.
N.B. Artificial intelligence can be used to straighten out definitions.
I have already heard it say wonderful things as long as we enter the
right data.

R.H.

As I tell the other idiots, if you want to change the definitions, go
ahead, just don't say you are working in the standard system.

IF you think the definitons are "false", then you don't understand how
formal logic works.

Sorry, you are just proving your stupidity.

Thank you for your post.

R.H.

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On 2/16/25 6:11 PM, Richard Hachel wrote:

Le 16/02/2025 à 21:50, "Chris M. Thomasson" a écrit :

On 2/16/2025 11:04 AM, Richard Hachel wrote:

Le 16/02/2025 à 19:39, Richard Damon a écrit :

On 2/16/25 9:27 AM, Richard Hachel wrote:

Le 16/02/2025 à 02:42, Richard Damon a écrit :

4 * i^4

Absolutely.

J'avais toujours dit que les Richard étaient des êtres exceptionnels. >>>>>
Nota bene:
4 * i^4 = -4

No, i^4 - 1, since i^2 = -1, by definition.

When definitions are incorrect, the definitions should be ignored.

Go ahead an ignore the complex numbers. Why should we care?

[...]

That's not what I said.
I spoke of "definitions" and not of "matter".
I was saying that false and lame definitions should be ignored, and
replaced by truer, clearer, more beautiful definitions.
It's not that complex numbers should not be studied, it's that if we
study them, we must study them correctly and with the right definitions.
Once that's done, everything that remains can be thrown in the trash.
Let's take the very definition of the entity i. Mathematicians propose definitions so ugly, even false, that it will make future generations
laugh.
It is these falsehoods and distortions that deserve to disappear.
I said the same thing about special relativity, and I am then considered
in several ways (a madman who denies everything, a crank who destroys
what is good).
All this is not very serious on the part of men.
N.B. Artificial intelligence can be used to straighten out definitions.
I have already heard it say wonderful things as long as we enter the
right data.

R.H.

As I tell the other idiots, if you want to change the definitions, go
ahead, just don't say you are working in the standard system.

IF you think the definitons are "false", then you don't understand how
formal logic works.

Sorry, you are just proving your stupidity.

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