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#3 TRUE CALCULUS; without the phony limit concept; Textbook for Middle-School on up (1st edition)
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Archimedes Plutonium
May 20, 2013, 2:13:53 AM5/20/13
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Now I must correct myself in the previous post I called it root-
pi*10^603 when it was floor-pi*10^603, at least that is what L.Walker
called it in posts of some years back.
And I must apologize for promising that my next book after the Atom
Totality was a geology book based on Maxwell Equations physics.
Trouble is that I keep having these thoughts on Calculus that I had
planned on doing the two concomitantly, but the thoughts of Calculus
keeps flooding me that I decided to do this now. If I wanted to, I
probably can write all 100 pages or less in just 24 hours, for I have
nothing new to discover, but just to write down what I already learned
in the book Correcting Math of 2011. It is that I wanted to write this
book about Calculus for I have it all assembled in my mind and no
point in waiting around.
So let me review for a moment here about the derivative. The
derivative is this angle top of the triangle of the picket fence
construction of the function. So for the function y=x that little
picketfence top of the triangle looks like this:
/|
||
where that picket fence top is 45 degree angle per the x-axis. In fact
the entire graph of the function y=x is a 45 degree angle to the x-
axis.
Now those angle tops can vary for each point of the function within 0
degrees up to but not including 90 degrees. If the angle top was 90
degrees it is no longer a function of mathematics so it has to be
smaller than 90 degrees. And the angle top can be 0 degrees such as
functions like that of y =3 since it is a graph of a line parallel to
the x-axis.
Now the derivative is rate of change, or slope or tangent. So why is
the derivative these concepts? Because it is an angle that can vary
from 0 up to 90 degrees and signifies how that function is changing,
and it does this by the fact that the Cartesian Coordinate System of
points are always the same relative to one another regardless of the
size of the graph. The numbers are all the same relative position from
one another whether it is a small graph paper or a large one. Size
makes no difference, so that the angle of 45 degrees for y=x is the
same no matter the size involved. It is this uniformity of spacing
arrangement of the numbers as coordinates that delivers the same angle
of 45 degrees in the function of y=x.
The angle of the picketfence top is the key to Calculus for if we want
rate of change, slope or tangent, it is this angle we ascertain from
the picketfence top at a specified point. If the angle is steep, the
rate of change is fast. If the angle is near 0 or 0 such as y=3, there
is little change going on.
The angle is critical also for the integral, since the integral is
area under the graph of the function and the area involves that angle
at the top to be precise area. We could just place thin rectangles
under the graph of the function and add up the area of all the thin
rectangles, but it would not be exactly the area, so we have to use
these picketfences to gain the exact area. And here we get a glimpse
of how the derivative is the inverse of the integral. So for the
derivative we want the angle at the top and for the integral we want
the area of the picketfence that includes that angle at the top.
Now let us review the function y = x^2 with its derivative of y' = 2x
so that for the point x=3, then y was 9, and the slope or tangent at
x= 3 was 6.
And we looked at the point to the left of 3 which is 2 and the point
to the right of 3 which is 4 to see that the change in y was 16-4
while the change in x was 4-2 which we have dy/dx as 12/2 = 6. But
what if we made the interval further apart from 3. What if we made the
interval from x=2 to x=5 then our dy/dx is
(25-4)/(5-2) would be 21/3 is 7, and 7 is not the exact derivative of
6.
So why did I bother with expanding the interval for the derivative of
y=x^2 at the point of x=3? Well, I wanted to show how important it is
to have a hole or gap between successive numbers and how the Calculus
cannot survive as mathematics if there was a continuum of numbers
between any two given numbers. That Calculus exists only when each
point has a gap or hole of its neighboring point on the left and on
the right. For the hole or gap allows that angle on top of the
picketfence to be free to swing around between 0 and 90 degrees for an
exact angle at that point, an exact derivative. When the derivative is
y'=2x then for x=3, the derivative must be 6 and not 7.
Now in Old Math, they had a continuum between any two points, and when
they had a function like the Weierstrass pathological function that is
continuous everywhere yet differentiable nowhere is simply in error
and not true at all. The Weierstrass function is actually and truly
continuous everywhere if we define continuous as having all gaps no
larger than 10^-603 and is differentiable everywhere. In fact, in New
Math all continuous functions are differentiable everywhere. Because
once you plot the points of 0 then 1*10^-603 then 2*10^-603 then
3*10^-603 all those jagged mountain tops of the Weierstrass function
disappear.
Which brings us to a very important message and conclusion which I
should make as the next chapter and call it the chapter that claims
all functions should be able to be plotted of all its points in the
mind. We should be able to see the plotting of all the points of a
function all at once in the mind's eye. We can do that already with
y=3 or y=x but at y=x^2 we begin to falter and with more complicated
functions we are lucky to plot a hundred points and guess at what the
rest of the graph looks like. In New Math, all functions should be
able to be plotted within the mind's eye. And why would I say that?
Because all the points of mathematics is this progression:
0, 1*10^-603, 2*10^-603, 3*10^-603, . .
So hand me any function. Hand me the Weierstrass pathological function
and I determine what 0 is, then 1*10^-603 is then 2*10^-603 and then
shortly there after I have what the whole graph of the function looks
like and I know it is differentiable at every point. In New Math,
every function can be zoomed in to a point and its neighbors. In Old
Math there were infinities everywhere which blinded those
mathematicians and forced them into silly and stupid fixes such as the
limit concept.
--
More than 90 percent of AP's posts are missing in the Google
newsgroups author search from May 2012 to May 2013. Drexel
University's Math Forum has done a better job and many of those
missing posts can be seen here:
http://mathforum.org/kb/profile.jspa?userID=499986
Archimedes Plutonium
http://www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
pi*10^603 when it was floor-pi*10^603, at least that is what L.Walker
called it in posts of some years back.
And I must apologize for promising that my next book after the Atom
Totality was a geology book based on Maxwell Equations physics.
Trouble is that I keep having these thoughts on Calculus that I had
planned on doing the two concomitantly, but the thoughts of Calculus
keeps flooding me that I decided to do this now. If I wanted to, I
probably can write all 100 pages or less in just 24 hours, for I have
nothing new to discover, but just to write down what I already learned
in the book Correcting Math of 2011. It is that I wanted to write this
book about Calculus for I have it all assembled in my mind and no
point in waiting around.
So let me review for a moment here about the derivative. The
derivative is this angle top of the triangle of the picket fence
construction of the function. So for the function y=x that little
picketfence top of the triangle looks like this:
/|
||
where that picket fence top is 45 degree angle per the x-axis. In fact
the entire graph of the function y=x is a 45 degree angle to the x-
axis.
Now those angle tops can vary for each point of the function within 0
degrees up to but not including 90 degrees. If the angle top was 90
degrees it is no longer a function of mathematics so it has to be
smaller than 90 degrees. And the angle top can be 0 degrees such as
functions like that of y =3 since it is a graph of a line parallel to
the x-axis.
Now the derivative is rate of change, or slope or tangent. So why is
the derivative these concepts? Because it is an angle that can vary
from 0 up to 90 degrees and signifies how that function is changing,
and it does this by the fact that the Cartesian Coordinate System of
points are always the same relative to one another regardless of the
size of the graph. The numbers are all the same relative position from
one another whether it is a small graph paper or a large one. Size
makes no difference, so that the angle of 45 degrees for y=x is the
same no matter the size involved. It is this uniformity of spacing
arrangement of the numbers as coordinates that delivers the same angle
of 45 degrees in the function of y=x.
The angle of the picketfence top is the key to Calculus for if we want
rate of change, slope or tangent, it is this angle we ascertain from
the picketfence top at a specified point. If the angle is steep, the
rate of change is fast. If the angle is near 0 or 0 such as y=3, there
is little change going on.
The angle is critical also for the integral, since the integral is
area under the graph of the function and the area involves that angle
at the top to be precise area. We could just place thin rectangles
under the graph of the function and add up the area of all the thin
rectangles, but it would not be exactly the area, so we have to use
these picketfences to gain the exact area. And here we get a glimpse
of how the derivative is the inverse of the integral. So for the
derivative we want the angle at the top and for the integral we want
the area of the picketfence that includes that angle at the top.
Now let us review the function y = x^2 with its derivative of y' = 2x
so that for the point x=3, then y was 9, and the slope or tangent at
x= 3 was 6.
And we looked at the point to the left of 3 which is 2 and the point
to the right of 3 which is 4 to see that the change in y was 16-4
while the change in x was 4-2 which we have dy/dx as 12/2 = 6. But
what if we made the interval further apart from 3. What if we made the
interval from x=2 to x=5 then our dy/dx is
(25-4)/(5-2) would be 21/3 is 7, and 7 is not the exact derivative of
6.
So why did I bother with expanding the interval for the derivative of
y=x^2 at the point of x=3? Well, I wanted to show how important it is
to have a hole or gap between successive numbers and how the Calculus
cannot survive as mathematics if there was a continuum of numbers
between any two given numbers. That Calculus exists only when each
point has a gap or hole of its neighboring point on the left and on
the right. For the hole or gap allows that angle on top of the
picketfence to be free to swing around between 0 and 90 degrees for an
exact angle at that point, an exact derivative. When the derivative is
y'=2x then for x=3, the derivative must be 6 and not 7.
Now in Old Math, they had a continuum between any two points, and when
they had a function like the Weierstrass pathological function that is
continuous everywhere yet differentiable nowhere is simply in error
and not true at all. The Weierstrass function is actually and truly
continuous everywhere if we define continuous as having all gaps no
larger than 10^-603 and is differentiable everywhere. In fact, in New
Math all continuous functions are differentiable everywhere. Because
once you plot the points of 0 then 1*10^-603 then 2*10^-603 then
3*10^-603 all those jagged mountain tops of the Weierstrass function
disappear.
Which brings us to a very important message and conclusion which I
should make as the next chapter and call it the chapter that claims
all functions should be able to be plotted of all its points in the
mind. We should be able to see the plotting of all the points of a
function all at once in the mind's eye. We can do that already with
y=3 or y=x but at y=x^2 we begin to falter and with more complicated
functions we are lucky to plot a hundred points and guess at what the
rest of the graph looks like. In New Math, all functions should be
able to be plotted within the mind's eye. And why would I say that?
Because all the points of mathematics is this progression:
0, 1*10^-603, 2*10^-603, 3*10^-603, . .
So hand me any function. Hand me the Weierstrass pathological function
and I determine what 0 is, then 1*10^-603 is then 2*10^-603 and then
shortly there after I have what the whole graph of the function looks
like and I know it is differentiable at every point. In New Math,
every function can be zoomed in to a point and its neighbors. In Old
Math there were infinities everywhere which blinded those
mathematicians and forced them into silly and stupid fixes such as the
limit concept.
--
More than 90 percent of AP's posts are missing in the Google
newsgroups author search from May 2012 to May 2013. Drexel
University's Math Forum has done a better job and many of those
missing posts can be seen here:
http://mathforum.org/kb/profile.jspa?userID=499986
Archimedes Plutonium
http://www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
hbe...@gmail.com
May 20, 2013, 8:56:55 AM5/20/13
to
Why this is marked as abuse? It has been marked as abuse.
Report not abuse
On Sunday, May 19, 2013 11:13:53 PM UTC-7, Archimedes Plutonium wrote:
> Now I must correct myself in
BAsically every single thing you have posted here.
> Now I must correct myself in
the previous post I called it root-
>
> pi*10^603 when it was floor-pi*10^603, at least that is what L.Walker
>
> called it in posts of some years back.
>
>
>
> And I must apologize for
that would be laughed-at by , well, anyone who knows anything?
By trying to make yourself into a big scientist and trashing this site in order to boost your ego (while fooling no one)?
> promising that my next book
not be completely useless and pointless.
after the Atom
>
> Totality was a geology book based on Maxwell Equations physics.
be completely meaningless.
>
> Trouble is that I keep having these thoughts on Calculus that I had
>
> planned on doing the two concomitantly, but the thoughts of Calculus
>
> keeps flooding me that I decided to do this now.
Why don't you wait until your stupid ideas go away? I too ; we all, have stupid ideas from time-to-time (tho I'm sure not as many as you do.). But most sensible people let go of their stupid ideas. You, OTOH, hold on to them as if your life depended on it.
> Trouble is that I keep having these thoughts on Calculus that I had
>
> planned on doing the two concomitantly, but the thoughts of Calculus
>
> keeps flooding me that I decided to do this now.
If I wanted to, I
>
> probably can write all 100 pages or less in just 24 hours, for I have
>
> nothing new to discover,
but just to write down what I already learned
>
> in the book Correcting Math of 2011.
1) You can post complete ,off-topic garbage in an unmoderated site
without any concern for other's rights?
2) That you can pass-off untested garbage as if it were true?
3)That no moderated site will accept anything from you?
4)That you can pump your chest like a chimp to make you feel good about the garbage that you write?
5)That you don't have the balls to submit your material to a critical audience?
6)That you can make repeated claims "about what Mathematicians do" without having any basis in fact?
It is that I wanted to write this
>
>>
>
>
> So hand me any function. Hand me the Weierstrass pathological function
>
> and I determine what 0 is, then 1*10^-603 is then 2*10^-603 and then
>
> shortly there after I have what the whole graph of the function looks
>
> like and I know it is differentiable at every point. In New Math,
>
> every function can be zoomed in to a point and its neighbors. In Old
>
> Math there were infinities everywhere which blinded those
>
> mathematicians and forced them into silly and stupid fixes such as the
>
> limit concept.
Yet again you show your ignorance, and how you make things up. There is a discrete version of the derivative, there is discrete differential geometry. But you claim you have an original view. You are a complete FRAUD.
>
> and I determine what 0 is, then 1*10^-603 is then 2*10^-603 and then
>
> shortly there after I have what the whole graph of the function looks
>
> like and I know it is differentiable at every point. In New Math,
>
> every function can be zoomed in to a point and its neighbors. In Old
>
> Math there were infinities everywhere which blinded those
>
> mathematicians and forced them into silly and stupid fixes such as the
>
> limit concept.
hbe...@gmail.com
May 20, 2013, 8:57:13 AM5/20/13
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On Sunday, May 19, 2013 11:13:53 PM UTC-7, Archimedes Plutonium wrote:
hbe...@gmail.com
May 20, 2013, 8:57:27 AM5/20/13
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hbe...@gmail.com
May 20, 2013, 8:57:33 AM5/20/13
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On Monday, May 20, 2013 5:56:55 AM UTC-7, hbe...@gmail.com wrote:
hbe...@gmail.com
May 20, 2013, 8:57:41 AM5/20/13
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On Monday, May 20, 2013 5:56:55 AM UTC-7, hbe...@gmail.com wrote:
hbe...@gmail.com
May 20, 2013, 8:57:48 AM5/20/13
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On Monday, May 20, 2013 5:56:55 AM UTC-7, hbe...@gmail.com wrote:
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