# Thread: Definition of the Derivative - h vs Delta x

1. ## Definition of the Derivative - h vs Delta x

To the reader: please read my ignore list before continuing. (If you understand calculus, the reason should be obvious) Neverfly and the Naked Emperor have spammed my thread beyond my level of tolerance personal invective, irrelevant comments, and I am no longer responding. The first post is a simple explanation of a common approach in defining the derivative. Pm me if you have any questions or need for discussion.
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To define a derivative one needs two orthogonal coordinate systems:

1. a global coordinate system (x,y) on which functions are defined (x,f(x))
2. a local coordinate system = (h,f(x'+h)-f(x')) = (x',y') that defines the tangent at the point h = (x - a) as x -> a (h -> 0) in the denominator of the definition of the derivative:

The confusion of h=x' with x (or x implies the mistaken concept that the slope is always related to the global coordinate system instead of moving locally to the tangent to f(x) as h-> 0.

(The point being that the tangent/slope changes in direction as well as magnitude as it approaches the limit)

The prescription of h instead of x' is shorthand for indicated the moving normal to the curvature as h shrinks to 0 at the point (x,f(x) of the global coordinate system.

(John Gabriel makes this conceptual error by defining h to be the same as x (which is always parallel to the horizontal axis of the global coordinate system), which is coupled with the error of m in the slope which contributes to his mistaken avoidance of curvature of f(x) and the resultant necessity of taking limits to define the tangent at an arbitrary point (x.f(x)) in the global coordinate system.

Update: Obviously, others on my ignore list and in this thread make this fundamental error as well.

(The point being that the tangent/slope changes in direction as well as magnitude as it approaches the limit)

See Derivative, derivative

At the limit at the point in question, the slope becomes in the local coordinate system, where x' is congruent to the tangent at the point in question (not parallel to the horizontal axis of the global coordinate system in which y = f(x) is defined.

(This corresponds to h (Planck's constant) going to zero along the curvature of a geodesic, in which case classical (non-quantum) physics applies conceptually (light has no mass according to Einstein in locally flat space-time) ...

2. ## Re: Definition of the Derivative - h vs Delta x

Originally Posted by BuleriaChk
To define a derivative one needs two orthogonal coordinate systems
One sentence in and you rae already wrong.

3. ## Re: Definition of the Derivative - h vs Delta x

Originally Posted by emperorzelos
One sentence in and you rae already wrong.
One sentence in and you show you have no idea how the derivative actually works, since you still imagine only one number line (like John Gabriel) completely ignoring the definition of function, Descartes, independent variables, not to mention curvature, Newton and all of physics and linear systems).

One should never try to teach a pig to sing; it is very frustrating, and only irritates the pig.

(sigh)

Oh, and good luck in your differential geometry class (if you ever make it that far)..

4. ## Re: Definition of the Derivative - h vs Delta x

Originally Posted by BuleriaChk
One sentence in and you show you have no idea how the derivative actually works, since you still imagine only one number line (like John Gabriel) completely ignoring the definition of function, Descartes, independent variables, not to mention curvature, Newton and all of physics and linear systems).

One should never try to teach a pig to sing; it is very frustrating, and only irritates the pig.

(sigh)

Oh, and good luck in your differential geometry class (if you ever make it that far)..
You're so cute I did that class a year and a half ago, passed with ease and doing reimann geometry now for fun! Already got my masters degree in mathematics.

I know how derivative work consideribly better than you, as a matter of fact in mathematics I know it much better than you in every regard you've opened your mouth. The issue is that you are so locked into your idea of geometry and such that you fail to see the bigger picture.

You instantly start with "orthogonal" without realising that things work in non-orthogonal systems and more importantly, that the term "orthogonal" doesn't make sense unless you start assuming inner-product spaces at which you've already made far far too many unneccisery assumptions. That is why I have told you to abondon the geometry garbage time and time again

has no orthogonal basis because it is just a set of elements, as a -vector space does have a basis but saying it is orthogonal in anyway is meaningless, as a -inner product space does have a base and it is meaningful to ask wether or not it is orthogonal or not which it doesn't necciserily need but is usually prefered.

Et cetera. You do not however need to call forth an inner product to define derivative and hence orthogonality is superflous.

You are so laughably pathetic that you must bring up that irrelevant list of yours, can't you be unlike Gabriel and grow you? As it is now you are just like him, nothing but a crank.

5. ## Re: Definition of the Derivative - h vs Delta x

Originally Posted by emperorzelos

(snip)
I'll let the knowledgeable reader judge for himself as to the relevance of the Naked Emperor's buzzword salad. The Naked Emperor insists on spamming my threads with pseudo bullshit, even though I have asked him to stay out of my threads. I'm not about to contribute to his; it would be a complete waste of time.

The Naked Emperor and has no analytic ability whatever, and is a PITA to any serious mathematician, not to mention physicist.

6. ## Re: Definition of the Derivative - h vs Delta x

Originally Posted by BuleriaChk
I'll let the knowledgeable reader judge for himself as to the relevance of the Naked Emperor's buzzword salad. The Naked Emperor insists on spamming my threads with pseudo bullshit, even though I have asked him to stay out of my threads.

The Naked Emperor and has no analytic ability whatever, and is a PITA to any serious mathematician, not to mention physicist.
So because I know more about mathematics and it's many structures that is used it is buzzword salad? That demosntrates quite well how ignorant you are. I can cite mathematical sources for it all, your stuff is painful to any mathematician, I know, it is painful to me.

THat is because you know nothing here. Go back and learn something

Inner Product space

A quick glance at wikipedia would have helped you.

Also if you want me to stay out of your threads, how about you stop saying stupid shit? As long as you do that I will always comment and expose your idiocy.

7. ## Re: Definition of the Derivative - h vs Delta x

In math and science, it is necessary to confront our ideas, methods, assumptions and motivations at all times. As frustrating and defensive as that may be, it is what keeps bias from rearing its ugly head.
Those challenges need to be met. Indeed, to not do so implies an inability to do so.

BuleriaChk, if you think that emperorzelos questions are not relevant, you need to show why you think so. Emperorzelos, if you think they are relevant, you need to show why they are. Defend your positions.

If it was so easy as simply disregarding any challenge to an idea, we would not have the sciences we have today.

8. ## Re: Definition of the Derivative - h vs Delta x

Originally Posted by Neverfly
In math and science, it is necessary to confront our ideas, methods, assumptions and motivations at all times. As frustrating and defensive as that may be, it is what keeps bias from rearing its ugly head.
Those challenges need to be met. Indeed, to not do so implies an inability to do so.

BuleriaChk, if you think that emperorzelos questions are not relevant, you need to show why you think so. Emperorzelos, if you think they are relevant, you need to show why they are. Defend your positions.

If it was so easy as simply disregarding any challenge to an idea, we would not have the sciences we have today.
I agree, I have however made posts showing their relevans as I believe you have seen.

9. ## Re: Definition of the Derivative - h vs Delta x

Originally Posted by Neverfly
BuleriaChk, if you think that emperorzelos questions are not relevant, you need to show why you think so. Emperorzelos, if you think they are relevant, you need to show why they are. Defend your positions.
His reference to inner product spaces is irrelevant, as any cursory examination of the definition of the derivative will show. (If you bother to look at the definition of the derivative.) In math and science it is important to learn about math and science. It is total bullshit, and based on his misunderstanding and rejection of orthogonal coordinate systems, starting with Descartes. Or starting from a subject in mathematics that is irrelevant to this thread. You might try doing some research yourself (in particular, Analytic Geometry).

Furthermore, the Naked Emperor's posts are loaded with personal attacks and invective. I might discuss Inner Product spaces if it weren't for that, but it is a subject for a different thread. It is an abstract concept, not relevant to the definition of the derivative.

Note: An inner product space is a linear space. Curves are non-linear. However, the approximation is linear, at a local point on the curve. As I said, the notation "h" is a short hand for the "neighborhood" concept - it is just a shorthand. The only distinction I am making is the x refers to a local coordinate system that rotates with the position on the curve, not global coordinate that defines (x,f(x)), as is obvious from any definition of derivative.

Google it, for chrissakes..... Or take a community college course in calculus.

10. ## Re: Definition of the Derivative - h vs Delta x

Originally Posted by BuleriaChk
His reference to inner product spaces is irrelevant, as any cursory examination of the definition of the derivative will show.
(If you bother to look at the definition of the derivative.) In math and science it is important to learn about math and science.
It is total bullshit, and based on his misunderstanding and rejection of orthogonal coordinate systems, starting with Descartes.
Or starting from a subject in mathematics that is irrelevant to this thread. You might try doing some research yourself (in particular, Analytic Geometry).

Furthermore, the Naked Emperor's posts are loaded with personal attacks and invective. I might discuss Inner Product spaces if it weren't for that, but it is a subject for a different thread. It is an abstract concept, not relevant to the definition of the derivative.
I reject nothing in mathematics. However what I told you is that the concept of "orthogonality" is meaningless unless you assume an inner product space which is true. Without an inner product the concept of orthogonality is meaningless in mathematics and derivative does not neccesitate an inner product space, all it does neccesitate is a normaed space by virtue of limits in standard analysis. Even there we can skip it if we choose to go to hyperreals. So the need for an inner product is superflous and in turn, orthogonallity.

Want me to cite sources for all? I even explained it in my earlier post, where even if we go by your love for cartesian product we do not have orthogonality garantueed.

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