Recent content by suremarc

If you have python installed and your PATH set up properly, simply typing “python” in your terminal should start the interpreter.

A friend of mine used to work at NYSE. The lead software architect there (his name is Alexei Lebedev) created a system that generates what is essentially a zero-overhead in-memory database in C++. You define your data in the form of tabular relations, and it knows how to generate efficient code...

Not an expert, but I know my way around some basic tensor math. Normally I would the tensor product in Einstein notation, ie ##A_{ijk}x^ix^j##. Then I would write the derivative as a tensor-like expression: ##\partial_i = \frac{\partial}{\partial x^i}##. And then we can apply it: $$\partial_l...

I think I've now figured out how I'm supposed to do it, but I seem to have "proven" in my original proof that , which contradicts what I'm reading. I will take a closer look.

I'm pretty unsure about this solution. Linear algebraic groups over finite fields is new territory to me, but I think I managed to leverage some of my abstract algebra knowledge.

This is exemplified in the geometric series, which was known to mathematicians centuries before Cantor. A “higher set of infinity” is still infinite nonetheless. There may be multiple infinities, but they are all infinite. It is meaningless to say something is “bigger than infinite” because...

If so, then he failed to follow up properly, because nowhere has he directly mentioned Zeno’s paradox in any form as far as I know. I think Cantor’s set theory helped advance set theory and topology by dealing with infinities, but the concept of limits and other constructions in analysis existed...

I’m not aware of a specific solution to Zeno’s paradox proposed by Cantor. Turbulent flows are well-known to have fractal-like properties. I’d say that fluid dynamics are “related” to set theory insofar as fractals are. It’s worth noting that fractals existed before set theory — they came up in...

I am guessing that the following leap $$\int_{-\infty}^\infty e^{-bx}(\cos(ax)+i\sin(ax))\,dt=\int_{-\infty}^\infty e^{-bx}\cos(ax)\,dz+i\int_{-\infty}^\infty e^{-bx}\sin(ax)\,dt$$ is not justified due to failure of absolute convergence (in some generalized sense that applies to distributions).

(1) is not a ring. Are you asking for four non-isomorphic rings? If so, I think this should be stated in the question. I was also iffy on (3), but Wikipedia says the notation is used outside of number theory. So I thought it was worth a shot.

Well, guess I’ll grab the low-hanging fruit: It would be a pleasant surprise to me if there were other meanings; I don’t know of any others.

Sorry, but I’m going to be straight and say that this post is really frustrating to read. How does a “growing alphabet” produce an algorithm? What does “exhaustive in terms of computability” mean? What is ##\mu## and what is God’s theorem? You cannot simply assume that we know what you mean...

I don’t understand what you mean in this last statement, but yes, I realize now I was mistaken. I was looking for an analog of Goodstein’s theorem for ZFC.

It might be more difficult than it looks, depending on what "blah, blah, blah" entails. For example, prove that ##\mathrm{BB}(n)## is total for ##n## between 0 and 100. (Which may not even be possible in ZFC.) But I suppose that proving 100 theorems is essentially as "difficult" as proving the...

Correct me if I’m wrong, but the quantifier ##\forall## applies to all sets, in the sense that for any model ##M## of set theory, the statement ##\forall x\,P(x)## quantifies over all elements of ##M##. Otherwise ##M## wouldn’t properly “model” the quantifier ##\forall##, would it?