1 William Kneberg, March 4, 2009 at 3:33 a.m.:

I know how the real numbers work, but what is the mathematics for each one, especially where you run into the irrationals, rationals, and ,01 (with a repeating zero that goes on forever), added to the number .9, with a repeating nine, and what are other numbers that act in a strange way? What are the mathematical rules, and what does it mean for mathematics and physics? What is the basis of discrete mathematics and how it applies to nature, in quantum theory, and with wave particle duality? If you have a quanta of mass moving along, it is discrete, if you have a wave, then it is linear, or atleast close to it, and how do these two get along mathematically? Am I right that one is discrete and one is linear? Also I have a interest in number one, and if it is also truth, then how does it work for both quantum physics, discrete mathematics, mathematical theory, truth tables, and the truth of logic? What is Cabala?

Right now I am studying CLEP and am wondering how logic basically works, without completely memorizing all of it. I see that there are definitions, postulates, theorems, axioms, corollaries, and inductive and deductive logic? I see that when the logical rules represent a collection of possible equations, it leaves only a few possibilities, that can later be refined into a specific equation to measure a phenomenon, with each situation being a pairing of data from different variables. This is where the rules of logic come in. If you have an implication, you have your hypothesis or premise and the conclusion in an if-then format, that can mathematically provide options for mathematical equations that can then be narrowed down, based on the result to a graph, where the data that is known, will project out new experimental sets of data that can be tested and then go to confirm the premise or hypothesis and the statement, if proven true will be able to be wound up coming to inductive and deductive logical conclusions that predict new experimental data. I have a vague grasp here, but I need to know the interface between theory and experiment and how all of it, in a simple format, works. If you can answer this I would be very happy to hear the answer or be directed to other resources or people to answer these questions.

Also, how does set theory work compared to logic. I understand that they are the "basis of mathematics" from what I read, but I don't see how the two being some different kinds of logical kinds of things can work together, and how they fit since I don't understand all of it from either side of the fence of logic makes me wonder what I should think about mathematics. If I can find an answer, I will be wielding quite a bit of power and knowledge in intellectual tools, and from there I can make more kinds of ideas and conclusions.

Sincerely,

William Kneberg