A lie is an approximate truth

A segment of a line contains infintely many points. For example the points of the interval [a;a+d] contains alef-null points for any non-vanishing d. Thus: You can't make a line by adding points. Accordingly the plane is not generated by adding lines, and so forth. The point, the line and the plane are sovereign enteties. But the integer correspondances are different. Integer means there are elements. I saw the surrealistic equation on the web:


1+1=3 , for large values of 1


It seems like nonsence, but actually your hand-held calculator may reckon like that. Here is the display (and also its memory):

It uses in fact integers. In this case ten digits for the mantissa and two for the characteristica. What is presented in the display is an interval - not a real number. After the "9" in the mantissa could follow infinitely many digits. These are truncated. When processing long series of calculation, one may get the surrealistic answer. This is only a result of how the machine works - not of mathematics. The Homer Simpson falsification of FLT is an example of false calculation. You can see it is wrong. On the left side there is an odd number and on the right side is an even. How can engineers build things that work, when they are using this false-calculating device? Because "real numbers" are not real. For every-day reckoning ten digits is satisfactory. No one has much use of numbers containing millions of decimals. Math, on the other hand, demands exact calculation. The mathematician wants to know if two enteties are equal, not if they are approximately equal. Hence the "transcendental" numbers. We can stick to the integers 1,2,3.... for a while. Not that I think it will be simple, but it will be "integral".

The sum of 1+2+3... is a "tiangle number"

The sum of triangle numbers 1+3+6... is a "tetrahedral number"

The sum of two consecutive triangle numbers is a "quadratic number" (The quadrate is not elementary in this weird math).

If there is something you can call a "cubic number", I have not found out yet.

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When looking at Wolfram, I gained some self-confidence. This is the first layer in a closed packed system. The second layer must have one point at "X". The third can have a point at eighter A or B. They correspond hexagonal (A) and cubic (B) close packing. Of course, this is seen from one specific angle. There are other angels making it easier to grasp. Building models is the best way to learn.