
What is a function #1 HSTextbook 7th ed. : TRUE CALCULUS; without the phony limit concept
Posted:
Jul 10, 2013 3:08 PM


What is a function #1 HSTextbook 7th ed. : TRUE CALCULUS; without the phony limit concept
The first ten pages of this textbook is devoted to High School (HS) students learning Calculus for the first time. The first ten pages is so well written that it requires no teacher, simply the interest and desire of a student to learn true Calculus, not the false and phony calculus with its limit concept.
Let us begin, and we define a function.
Definition : A function is a graph where every x value has a unique, one and only one y value.
A line segment or line can be a function because for every xvalue, there is just one and only one yvalue. But a square or rectangle or circle or ellipse drawn on a graph cannot be a function because for some xvalues, they have more than one y value.
Now the circle, if cut in half could be a function because for every x value, it can have one and only one yvalue.
Now we plot three functions in the 10Grid Coordinate System and using the 1st quadrant only. Throughout this textbook we plot only in the 1st quadrant with positive values for x and for y.
Definition: 10 Grid system is where we use all the counting numbers from 0 to 10 and where we use only 1/10 decimal fractions. And we thus have 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, . . on and on till we come to 10.0 and the Grid are points of these numbers looking like this:
. . . . . . . . . . . . . . . . . . . . . . . . . 0 .1 .2 .3 .4 xaxis
We are going to use three functions:
y = 3
y = x
y = 1/x
And the 10 Grid system is where we pretend 10 is infinity borderline and so all the numbers that exist in 10Grid are
0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, .. on up to the number 10
Not counting 0, there are 100 numbers along the xaxis, and likewise there are 100 numbers along the yaxis.
Now get a sheet of graph paper and plot these three functions with me:
y= 3 looks like this:
 ..........................> y=3   ...............................> xaxis
The function y=x looks like this where the diagonal splits the 1st quadrant in half:   /  /___
The function y = 1/x looks like this:
. x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x . . . . . . . . . ??? x . . . . . . ? ? x . . . . . x . . . . . . . . . . . . 0 .1 .2 .3 .4 .5
The student is going to need graph paper and pencil and erasure so as to keep on reusing the graph paper. Since ascii art on the sci.math newsgroup is difficult, the student must follow along by doing the graphs.
There is a famous pragmatist school of thought that "learning is in the doing" and this text requires the student to do, along with read.
 More than 90 percent of AP's posts are missing in the Google newsgroups author search archive from May 2012 to May 2013. Drexel University's Math Forum has done a far better job and many of those missing Google 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 electrondotcloud are galaxies

