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#26 2012-12-27 09:15:59

bob bundy
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Registered: 2010-06-20
Posts: 6,120

Re: What is the point (ordered pairs) of Graph of a function?

You jumped a long way in lesson 2, but I think I have it.

I have a point on a graph.  This point is infinitesimally small.  A tangent is drawn at the point.

See my picture.

Please go on.

Bob

View Image: lesson2.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#27 2012-12-27 10:19:27

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: What is the point (ordered pairs) of Graph of a function?

The equation of the tangent line:

-

Value of a derivative in a contact point the tangent line with graf on function.

You understand this?


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#28 2012-12-27 11:04:56

bob bundy
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Registered: 2010-06-20
Posts: 6,120

Re: What is the point (ordered pairs) of Graph of a function?

so equation of tangent is

Therefore equation is

Hope that is what you were trying to achieve.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#29 2012-12-27 11:35:25

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: What is the point (ordered pairs) of Graph of a function?

bob bundy wrote:

Bob

No!  tangent line  has no direction!


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#30 2012-12-27 11:56:57

bob bundy
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Registered: 2010-06-20
Posts: 6,120

Re: What is the point (ordered pairs) of Graph of a function?

What?

Why do you say this?

All lines have direction.

Please check your translation.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#31 2012-12-27 12:33:03

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: What is the point (ordered pairs) of Graph of a function?

I am sure by BOB soon all of you will understand. If on OX and OY to postpone identical sizes, for example:





that the area turns out isomerous and value of all points identical.

If you a cube decided

to represent in the form of a rectangle

that on the area there will be distortions and not all points will be identical and the directions equal. If you it understand that you will appear halfway to truth.

Last edited by 21122012 (2012-12-27 12:33:26)


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#32 2012-12-27 21:25:46

bob bundy
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Registered: 2010-06-20
Posts: 6,120

Re: What is the point (ordered pairs) of Graph of a function?

Good morning 21122012,

Some advice about teaching:

Lesson one was post 22.  I understood that

Lesson two was post 26.  You went a bit far for me but again I understood it.

Lesson three was post 28.  I thought I understood it perfectly.  I reproduced all your missing working.  Most teachers would have been delighted.

Lesson four was post 29.  It seems I have understood nothing.  You tell me something that I know is wrong.  So I ask for clarification as I think we have confusion over a word.

Lesson five was post 31.  This has nothing to do with what we have been doing.  You introduce many new functions.  You ignore my confusion completely and expect me to understand you.  I DON'T.  Please explain:

tangent line  has no direction!

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#33 2012-12-28 07:15:29

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: What is the point (ordered pairs) of Graph of a function?

bob bundy wrote:

Good morning 21122012,

  You ignore my confusion completely and expect me to understand you.  I DON'T.  Please explain:

tangent line  has no direction!

Bob

Good night bob bundy.

The main lesson was post 27. You ignore this lession. What in it it isn't clear to you?


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#34 2012-12-28 07:33:31

bob bundy
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Registered: 2010-06-20
Posts: 6,120

Re: What is the point (ordered pairs) of Graph of a function?

tangent line  has no direction!


????

Here is a horizontal line.  It has the direction left to right.

horizontal_A.jpg

Here is Cerry urging us to go in the direction North.

go-north.jpg

Here is a line that goes in a direction, 45 degrees to the axes.

45-degree.gif

I want to know how a tangent line can have no direction.  Please answer this question.

I have not bothered to look at your link again, because I don't understand it.

Let's take small steps.

Bob

View Image: direction.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#35 2012-12-28 08:10:31

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: What is the point (ordered pairs) of Graph of a function?

bob bundy wrote:

tangent line  has no direction!

????

Here is a horizontal line.  It has the direction left to right.
Bob

You as well as Calculus try to mix graphic objects and geometrical objects. Geometrical objects exist in isomerous space and graphic in the anisomeric.

I will show you distinction between graphics and geometry schematically on the example of cone and cylinder volumes as radius functions. If you don't comprehend sense then I in detail everything I will explain. You look:

http://vladimir938.eto-ya.com/files/201 … inder1.jpg


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#36 2012-12-28 08:20:42

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,658

Re: What is the point (ordered pairs) of Graph of a function?

Geometrical objects exist in isomerous space and graphic in the anisomeric.

No one ever heard of isomerous space and anisomeric is a term used in chemistry. Your use of jargon is just awful.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#37 2012-12-28 08:27:15

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: What is the point (ordered pairs) of Graph of a function?

bobbym wrote:

Geometrical objects exist in isomerous space and graphic in the anisomeric.

No one ever heard of isomerous space and anisomeric is a term used in chemistry. Your use of jargon is just awful.

I am not guilty in that that the mathematics didn't think up other term.

She thought up as the area of a circle

to represent in the form of a piece

and the term which displayed the curvatures connected with it didn't think up. Let's think out!:D


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#38 2012-12-28 08:29:15

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,658

Re: What is the point (ordered pairs) of Graph of a function?

You make up your own definitions, tangents do not have direction, points are small circles, you make up your own notation, your own definitions , your own words.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#39 2012-12-28 08:33:45

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: What is the point (ordered pairs) of Graph of a function?

bobbym wrote:

You make up your own definitions, tangents do not have direction, points are small circles, you make up your own notation, your own definitions , your own words.

And what to do if the mathematics can't precisely define expression:

It is necessary to think out that this distance between the next points.


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#40 2012-12-28 08:40:14

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,658

Re: What is the point (ordered pairs) of Graph of a function?

You do not even understand the difference between the discrete and the continuous. There is nothing wrong with the way
math is viewing either of those. What is wrong is that you refuse to read up on it. Refuse to listen to anyone.

Δx can be used as an approximation to dx when it is very small. Δx is not the same as dx, if it were there would not be two symbols. Differences are sometimes used as an approximation to the derivative. No one says they are equal.

You can not go around making up your own terms, definitions and notation. Yes, I know all the mathematicians missed it and you found it.

I am not guilty in that that the mathematics didn't think up other term.

You are guilty of creating terms that you have not defined. Of course no one can follow that.

How about giving us a rigorous definition of "isomerous space" or anisomeric space before you go on posting anymore.

What is apparent is you do not know very much about calculus or analytical geometry, that's okay, neither do I. But before I go shooting my big trap off about how dumb Isaac Newton is, I would do a little more research than you have.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#41 2012-12-28 09:02:41

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: What is the point (ordered pairs) of Graph of a function?

bobbym wrote:

You do not even understand the difference between the discrete and the continuous...

Δx can be used as an approximation to dx when it is very small. Δx is not the same as dx, if it were there would not be two symbols. Differences are sometimes used as an approximation to the derivative. No one says they are equal.

Any continuous is not understood discrete. Of it we are convinced by real sciences: physics, chemistry, etc.

Everything is accurately defined. It isn't necessary to think out more than anything!


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#42 2012-12-28 09:13:54

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,658

Re: What is the point (ordered pairs) of Graph of a function?

Just because as a limit that is true that is not the same as saying Δx = dx.

And what does that have to do with your so called isomerous space? You do not have a definition for that do you?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#43 2012-12-28 09:21:25

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,120

Re: What is the point (ordered pairs) of Graph of a function?

It is you who do not understand. 

7 times you have asked me what it is I don't understand on this thread and the other.

7 times I have told you.

Each time you tell me a new thing.

That is no help to me.

If you don't answer my questions I shall give up on your thread.

How can a tangent have no direction? 

Your answer should start: "A tangent has no direction because .........."

Last time of asking.

Thank you in anticipation,

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#44 2012-12-28 09:39:14

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: What is the point (ordered pairs) of Graph of a function?

Well !!!

I will show it on the example of the y=x^3 function you look link the tangent line is emphasized with a green strip and is one of other structural lines:

http://vladimir938.eto-ya.com/files/2012/11/alg.jpg

A tangent line has no direction because:

This line on graph of function

is set of all points lying on one line and dividing a piece

on two parts. Therefore this line anywhere doesn't begin and anywhere doesn't come to an end and has no direction.

You understand?

Understand one very important key point: when you decide to draw the Graf of function

and to represent the areas of circles

in the form of lengths of pieces you go on unforeseen distortions of further creation of the schedule which differ from geometrical reality.

Last edited by 21122012 (2012-12-28 09:39:32)


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#45 2012-12-29 08:37:10

bob bundy
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Registered: 2010-06-20
Posts: 6,120

Re: What is the point (ordered pairs) of Graph of a function?

I regret that I can make no sense of this.

Refer to my post on your original thread.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#46 2012-12-29 10:27:10

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: What is the point (ordered pairs) of Graph of a function?

bob bundy wrote:

I regret that I can make no sense of this.

Refer to my post on your original thread.

Bob

Whether it would be interesting to learn there were such people at the time of Galileo Galiley who looked in his telescope and spoke: "But I there see nothing! " Probably were...
dunno


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#47 2012-12-29 11:54:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,658

Re: What is the point (ordered pairs) of Graph of a function?

You are now comparing yourself with Galileo?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#48 2012-12-29 12:20:13

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: What is the point (ordered pairs) of Graph of a function?

bobbym wrote:

You are now comparing yourself with Galileo?

No! With Giordano Bruno

sad


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#49 2012-12-29 12:23:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,658

Re: What is the point (ordered pairs) of Graph of a function?

I am sorry you feel like that. But no one has burned you at the stake. You on the other hand have insulted and ridiculed others. You are the one who is peering through the telescope and saying. " I can't see anything!"


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#50 2012-12-29 13:03:55

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: What is the point (ordered pairs) of Graph of a function?

Strange. Show me where I did such bad things unworthy Giordano? And that that my posts and even topics everywhere mercilessly delete it and there is that that me with him similar.


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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