discrete mathematics

Hi

All well with you?

Do you know the logistic function which can be continuous. It's starting as an exponential growth the growth stops as an upside down exponential growth. An S-curve, somewhat stretched.

A relatively easy formula. Not so special. But the time is continuous.

And already famous is the discrete logistic function. That means now we do steps in the time. And WOW! What an interesting function it becomes. Please google for it. There's much to tell about. Just because we have made it discrete, so with steps and not continuous. Due to the discrete nature it becomes interesting.

Google can show a lot.

Continuous in an extension of discrete. Rational numbers have the same cardinality as integers. That is easy to see. Look at the two dimensional plane, with integer coordinates. Say x and y and those x and y are integers or whole numbers. But we can look at the positive quadrant as well.

Each rational number is a quotient x/y with y not 0. So each rational number is point of our x-y plane.

And we project that plan on the integer line. Just following the edge. and the only the right and top edge. (with the whole numbers. We would make growing squares around 0,0. So just with squares from 1 times 1 and then 2 times 2. And so we go further. And in the mean time in each step we project all border points on the Natural numbers. A limited square has always a limited number of integer coordinates so we can always project that on one line with integers.

Is this clear. And Q is sufficient in the sciences, and in the computer world.

1. In a real number we could also store everything. So that is a paradox.

2. We have the choice axiom of at once infinite choices. And there's the Banach-Tarski Paradox
That means with the choice axiom we can divide the solid unit sphere into two the same unit spheres. In the mathematical subject proof theory we can make that exact 1 = 2. Funny for sure.

But many people don't want to lose the axiom of choice. Indiscrete we don't have that problem that's a wider world.

3. The 3-body problems deals als with a space of Real coordinates. And noone has found a solution.

I can show you a paper on the net open for everybody. As soon as we take the time discrete in steps even very small steps will do. And suddenly it becomes high school mathematics. Just by making it discrete. Then the n=body problem is over as well. As soon we accept the wider solution space of also rows of numbers that we always can approximate when we want that. And such problems are over.

4. The discrete logical function is used in PRNGs (pseudo random number generators).

5. Do you know of discrete mathematics. One step further we have inductive mathematics and i will provide you with an inductive play that has become famous as well.

This is a link about that inductive play.

Inductive means we have information and we have to try to find the rule. So this is not having axioms and proof things from that. But now we have information and we have to find the rule.

It's a nice play for people with brains. The play has a leader and he or she has to make it very easy for the other for everyone has to learn it.

So many leaders make to difficult rules in the beginning. Maybe you now it already. It's Eleusis.

http://nnw.berlios.de/docs.php/intro-eleu/noflash

Please have a nice day

ed
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