Recent content by Data

You can, of course, construct polynomials that will give you all the primes up to any arbitrary point, if you already know what they are!

Your reply is a bit late. :wink: Still having a website that can perform calculator functions should not be that hard. I imagine flash can emulate the ti-83 online pretty well

Of course, to mathematicians algebra refers not to simple symbolic manipulation but to a huge class of subjects. You can divide mathematics roughly into three branches (though there's so much overlap and so many topics that don't quite fit that this is not a great guide): Analysis, algebra, and...

You know m 1_R=0_R. You need to show that there are some x, y in R with x\cdot (n 1_R) = 0_R and (n 1_R) \cdot y = 0_R. I suggest trying y=x = \frac{m}{(n,m)}1_R. :smile:

ahahah, that one's good :smile:

If \sqrt{c} is rational it's easy to see \sqrt{a}+\sqrt{b} must be rational. Then \sqrt{a} = r - \sqrt{b} where r is rational, ie. a = r + b - 2r\sqrt{b}, from which it follows that \sqrt{b} is rational (and the same argument shows \sqrt{a} must be rational as well).

If \sqrt{c} is rational it's easy to see \sqrt{a}+\sqrt{b} must be rational. Then \sqrt{a} = r - \sqrt{b} where r is rational, ie. a = r + b - 2r\sqrt{b}, from which it follows that \sqrt{b} is rational, and from that it follows that \sqrt{a} must be rational as well.

Reminiscent of the ever-popular "There are 10 types of people: Those who understand binary, and everyone else."

If you think you've come up with something new, I encourage you to write it up in some cogent form. I'll be happy to read it! :smile: I am just trying to warn you that unless you spend some time with real mathematical and physical literature (in the form of textbooks, published articles...

Indeed. While it's easy to say that highly theoretical courses are a priori harder than experimental stuff, there's one fact that breaks that argument completely, at least in my case: If I look at my audit (for a math-physics double honours degree), my grades in physics courses with a lab...

Yes, it is difficult to make visual representations of four-dimensional objects in 3- or 2-dimensional space (though it is certainly possible - see tesseracts and, for that matter, penteracts), and is quite perilous to try to visualize higher-dimensional objects; However, the arithmetic and...

A square root is an exponent, though! \sqrt{a} = a^{\frac{1}{2}}. If you understand the rules for exponents then it's easy to see how to square a square root. :wink:

Well, x^x = e^{x\ln x}, so it suffices to look at \lim_{x \rightarrow 0^+}{x \ln x} = \lim_{x \rightarrow 0^+}\frac{\ln x}{\frac{1}{x}}; Apply l'Hopital.

It sounds like you really are getting more into your math courses than your current major. What textbooks have you been using? I'd suggest picking up a few top-notch textbooks from the library; Say, Spivak's "Calculus," (this will cover things that you already know, but from a much more...

White Rabbit: Consider \sqrt{2}. What's (\sqrt{2})^2?