Recent content by Credulous

I'm looking for a function to plot things in 3D using cylindrical coordinates but apparently Mathematica doesn't have one?

So in essence, that would mean any combination of both sets, they would all contain factors of 8. So that would mean $$4\mathbb{Z}*2\mathbb{Z}=8\mathbb{Z}?$$or more generally: $$ m\mathbb{Z}*n\mathbb{Z}=mn\mathbb{Z}?$$

The definition of the Product of ideals I and J is $$IJ = \{a_1b_1+a_2b_2 + ...+ a_nb_n | a_i \in I, b_j \in J, n \in \mathbb{N}\}$$. But for say 4Z*2Z inside Z, how is the index "n" defined? I just don't get it. If you have $$2\mathbb{Z} = \{0, 2, -2,...\}$$ and $$4\mathbb{Z} = \{0, 4, -4...

I have to choose which math course I'm going to take next term. I want to take both but I'm already taking two physics courses and my college's distribution requirements require that I take an English next term... bleh... I could audit one of the physics and then take both math courses, but that...

whoops! This article that I found on arxiv: http://arxiv.org/abs/1204.0351

Specifically what Physics subjects and what mathematical techniques come into play that I would need to learn in order to comprehend it? I am currently in sophomore level undergrad physics (this year we covered waves, optics, ordinary differential equations, electromagnetism again, ect). I...

Are you talking about actual quotes from famous scientists or cool sounding names?

I was wondering what the majority opinion was on this issue, among physicists and philosophers as well. I can't imagine zooming in a million times smaller than the plank length and still not being at a smallest length, however a discrete universe doesn't make much sense to me. Are there any...

No, I wouldn't say that the brain is a computer, at least in the way that we currently understand and build computers. The brain is structured in what has been called a neural network. But I think that how the brain computes is irrelevant to the fundamental question of free will, so long as we...

Hmm, surprised I haven't seen, "Will to Reproduce". Or whatever signal that the brain interprets will lead to reproduction.

This is the way I see it: How do we know that Joan "chose" to be burnt at the stake? Well for one we know she told whoever was persecuting her that she would rather be burned at the stake than change her faith. And to tell them she had to open her mouth, inhale, and then exhale while moving the...

Hmm, well you know you can cancel the x to get: $$x \sin{\frac{1}{x}}.$$ From here it is just the sandwich theorem, we know $$ -1 \leq \sin{\frac{1}{x}} \leq 1 $$ so then $$\lim \limits_{x \to 0} -x \leq \lim \limits_{x \to 0} x \sin{\frac{1}{x}} \leq \lim \limits_{x \to 0} x$$ And you can...

What is the probability that a number selected from 0-9 will be the same number as one randomly selected from 0-4? Relevant equations: $$P(A \cap B) = P(A)*P(B|A)$$ I used the equation above, using A as the event that the number selected from 0-9 will be between 0 and 4, and B as the event that...