Recent content by baker0

Right, I was trying to prove this rigorously.

Presburger Arithmetic is not a good example. I claimed this was true for finite axioms.

Bohm certainly thought our universe was a hologram. Whether or not our universe is a hologram is currently highly unclear.

I don't think he will die anytime soon. He seems to be paranoid enough, that he'll kill off anyone he suspects of treason. If he were assassinated by foreign powers, he would be replaced with someone just like him. Just like he did. In other words, business as usual, as Greg pointed out.

You can't use 0 as a since 1/0 is undefined. That must be excluded from your answer.

Incompleteness has everything to do with axioms. Axioms do not prove themselves. Axioms are things that are assumed to be true. Axioms are just propositions. In order to be complete, we must prove these axioms.

True, you do have to be a little more rigorous. By incomplete I mean you cannot prove all the axioms to the point where nothing is left assumed or unproven. Of course Presburger Arithmetic is complete in the sense that you can deduce each proposition from the axioms. However, incomplete in that...

Is any collection of axioms incomplete? This seems to be intuitively true. Relating to Godel's Incompleteness theorem, Godel proved any consistent set of axioms based on the theory of natural numbers cannot be proved themselves, without leaving any assumptions. So what I am wondering is...

In addition, be careful about the first statement that you made. -xn≠(-x)n does not hold for all n and x that you are used to using. This statement is FALSE for all odd n. There is also some x for which this is false.

This is the real argument here. As economicsnerd pointed out, for a family of statements f(n), where n varies over a nonempty collection of the positive integers, if one of these statements is false, then there is a first false statement. Why is this the case? This follows from the fact that a...

Yeah, I thought it was odd that QM was not required, but some QM is covered in the modern physics course.

Currently, I'm doing a double major, one of which is a B.S. in physics. Of the following four classes, I have to take two of them. What I was wondering was which of these would be better preparation to enter grad school? Here the physics electives: -Introduction to Quantum Mechanics...