Formalization of sqroot definition

[CRGreathouse]

Assume x is negative. Then (-x) is positive, and (-x)^2 = x^2. We may apply the statement just proven to obtain f(x^2) = f((-x)^2) = abs(-x) = abs(x).

f(0) = 0 = abs(0), by the definition of f.

These three statements together show that f(x^2) = abs(x).

WHEN X<0 THEN abs(x)=-x AND NOT abs(x) = x
LEARN THE DEFINITION of the absolute value of a REAL No

uman didn't claim that abs(x) = x for x negative, just that abs(-x) = abs(x).

 

[peos69]

arildo your proof is right but where is the formalization of the definition??
Now we started getting somewhere

 

[peos69]

uman didn't claim that abs(x) = x for x negative, just that abs(-x) = abs(x).

HE DID the fatal mistake to use a formula which he proved ONLY FOR X>=0
definitely his formula does not apply for x<0,unless he proves (assuming he proves),
that f(x^2)= -x

 

[peos69]

After all this, you want to give peos another chance? What if you find out that peos made another unacknowledged notation error 3 pages too late? Why waste your time?

HOW MANY have i done up to now??
NAME them

 

[peos69]

Peos you seem to be convinced that you are right and all of us are wrong. Unless you can clearly explain your problem instead of repeating that our mathematics is not right, I don't think anyone can help you.

Definitely i have no problem the problem is yours that you cannot give a proper formalization of a h.school concept
You must also remember i did not discovered the sqroot

 

[arildno]

arildo your proof is right but where is the formalization of the definition??
Now we started getting somewhere

What nonsense are you talking?
My definition is perfectly formalized, in that particular format known as plain, English language.

 

[Gokul43201]

HOW MANY have i done up to now??
NAME them

Try these for size:

1)for all x sqoot (x)^2 = absolute value (x)

And several posts later...

let x=-3 then sq root(-3)^2=sq root(9)=3.

Both have parentheses in the wrong place. This was pointed out more than once, and you've chosen not to acknowledge it.

And quit with the capitals already, if you don't wish to get booted from here.

 

[peos69]

What nonsense are you talking?
My definition is perfectly formalized, in that particular format known as plain, English language.

FORMALIZATION IS FREE from any language that's the beauty of it

 

[arildno]

FORMALIZATION IS FREE from any language that's the beauty of it

Nonsense.
Besides, I note that you didn't bother to heed Gokul's WARNING.

 

[HallsofIvy]

I suspect that one problem is that after 68 posts in this thread you have never said exactly what you mean by "formalization".

 

[peos69]

:



, if you don't wish to get booted from here.

nice expression,good english

 

[uman]

peos69: Which part of my post only applies to x >= 0? The definition of f? That's true, but in high school I don't think most students learn about the square root of negative numbers; that is, they consider the square root function as a real-valued function. It would not be too difficult to extend my definition and proofs to make f complex-valued, and defined everywhere on R.

are you saying that I only proved that f(x^2) = abs(x) if x>=0? You are mistaken. I proved first that f(x^2) = abs(x) if x>0, then I used that fact to prove that f(x^2) = abs(x) if x<0. Then I pointed out that f(0) = 0. So,
If x > 0 f(x^2) = |x|
if x = 0 f(x^2) = |x|
if x < 0 f(x^2) = |x|. So in all cases, f(x^2) = |x|.
Do you see any specific problems with my proof? Or any other problems with the theory of the square root function that I developed in my post? I wrote it at about three in the morning and may well have made some mistakes!

Also, what precisely do you mean by "formalise"? I think if you made that clear we would be able to help you much better.

Please answer ALL the questions in this thread before posting again.

 

[berkeman]

nice expression,good english

peos69, Gokul is pointing out that we have Rules here on the PF, and it all works best if we check our attitudes at the door, and discuss the math and physics in a straightforward way. The Mentors are monitoring this thread, obviously.

 

[peos69]

Is it in your rules to use expressions "if you don't wish to get booted from here"
I am surprised.

 

[berkeman]

Is it in your rules to use expressions "if you don't wish to get booted from here"
I am surprised.

It is a common expression in English, and not considered rude in this context. Just keep a calm attitude, and focus on the math and the physics. And as Gokul was pointing out, all capital letters is considered yelling in the context of forum discussions, and should be avoided.

 

[peos69]

can i then in a common expression in English say to him boot yourself?
capital letters are considered for emphasizing things

 

[CompuChip]

You can emphasize things using italics with the [ i] [/ i] tag (without spaces), for example. That is already a lot nicer (and using Control + I, no more work than pressing Caps Lock twice).

the problem is yours that you cannot give a proper formalization of a h.school concept

The problem is not mine, because I am perfectly happy with my "formalization". If you are not, you should specify what you mean by a "formalization" (as pointed out repeatedly) and what there is as a "concept" to the square root.

 

[berkeman]

can i then in a common expression in English say to him boot yourself?

No, at this point that would be rude. It has nothing to do with the math and physics of this thread. He was pointing out the fact that you could receive infraction points for the aggressive nature of your posts. You would not be pointing out anything useful with the reply that you propose.

capital letters are considered for emphasizing things

Not in the context of web forum discussions, especially not the way you used them.

This thread appears to have run its course. Thread locked.

 

[HallsofIvy]

Note that "boot yourself" is quite different in meaning from "booted from here". The first implies physical violence while the second doesn't.

What has happened so far is that many people have given different types of "formalization" of the square root function and you have rejected them all. Will you please tell us what you mean by "formalization"?

 

[berkeman]

Will you please tell us what you mean by "formalization"?

Actually, that might be kind of hard for him. I already locked the thread. It's probably best to just let it lie, unless you want to unlock and carry on. I'm fine either way.