What is a function #1 HS-Textbook 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 x-value, there is just one and only one y-value. But a square or rectangle or circle or ellipse drawn on a graph cannot be a function because for some x-values, 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 y-value.
Now we plot three functions in the 10-Grid 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:
The student is going to need graph paper and pencil and erasure so as to keep on re-using 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: