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I will use the material in discrete math class, as reference for Math logic.
The proofs are very clear
Used in course
10 years ago
Many scientists believe in, what is called pantheism, the idea that the complex working of the nature around us is the only palpable God we can deal with. For this reason, Reality is the name used by philosophers to discuss God, so that the highly emotional content that goes with the word God can be avoided. From this it should be clear that reality is the same as metamathematics. Most philosophers agree that contemplation of Reality is the highest form of happiness. So, if you want happiness, play Metamath Solitaire all by yourself.
The applet Metamath Solitaire lets you build simple mathematical proofs from axioms in logic and set theory. This applet is based on a program called Metamath, which can express theorems in abstract mathematics, accompanied by proofs that can be verified by a computer program. Looking at Metamath, confirms many of my beliefs. Beauty, simplicity, and rigor are the same. You can trust a computer more than a mathematician. You must accept the four color conjecture, instead of quibbling about it. All proofs of all mathematics can be arranged in the lexical order in The Book, the amount of paper available being the only limitation (see White Hole, Black Whole and The Book, in Merlot, Foundations of Mathematics).This means that you can read The Book and collect as many theorems as you want, but don't ask for a solution to your conjecture. There is no good mathematics that a good high school student cannot understand. Any problem which has a solution, has a simple solution. It is not enough to define empty set, you must define the Void, when not even the empty set is there,
of course, Void is not a set, but we need the name. If we have Void, we can call a Dedekind cut a Void. If we have Void, we can answer the uncomfortable question, What was there before the Big Bang?, the answer is of course Void. It is not enough to define cardinals, we want the Absolute, which contains all the cardinals. Of course, Absolute is not a set (fortunately for us, Cantor has accepted this fact).