Recent content by Kamataat

What is the "field with one element"? From the definition of a field, it follows that such a thing does not exist. However a Google search reveals that apparently there is, or at least mathematicians think there ought to be, something that goes by that name. What is it? Is it called a "field"...

I suppose you can use \int\frac{a}{b\pm x}dx=\pm a\ln|x\pm b| - Kamataat

Remember that dx=d(x+c), c=const. - Kamataat

For the first one, the answer (\log_q2=p/4) is OK, but I have trouble understanding what you wrote before that. For the second one, you can't assume that 16=8q. Otherwise, you're on the right track: \log_q(8q)=\log_q8+\log_qq=3\log_q2+1 You already know what \log_q2 is in terms of p, so...

OK, I apologize for this mess. Feel free to delete that posting of mine. More careful next time. - Kamataat

A union of sets is composed exactly of the elements of those sets (no more, no less). Let's say we have the sets A=(a,b) and B=(c,d), where a<b<c<d. If their union were closed, then it would have to a) include "more" elements than there are in A and B, for example their endpoints OR b) include...

Prove by induction that 2^{2^n}+1 always ends in 7 for all n > 1 (true for n = 2). I couldn't figure out anything to do with the last digit being 7, so I looked the case that 2^{2^n} ends in 6 for all n > 1, which is also true for n = 2. Suppose it's true for n = k: 2^{2^{k+1}}=2^{2^k\cdot...

I think s/he means \lim_{\max\Delta x_k\rightarrow 0}~sum=L - Kamataat

Never heard of those terms, but if T-line is the tangent then N-line is the normal line (the line perpendicular to the tangent at x=-4) I suppose. - Kamataat

FS is vector directed away from the origin of the field. The magnitude of a resultant vector can be smaller that the magnitudes of the vectors being added. - Kamataat

You sure you calculated correctly? For the sun I get F=G\times\frac{M_{sun}}{(\frac{r}{2})^2}=6,672\cdot 10^{-11}\times\frac{7,67\cdot 10^{30}}{(\frac{2,72\cdot 10^{11}}{2})^2}=2,767\cdot 10^{-2}\frac{N}{kg} - Kamataat

Calculate the sun's grav. field magnitude at r/2 and then the planet's at r/2. Add these to get the total. - Kamataat

Thank you! - Kamataat

So if a question asks to find the speed which a body must achieve at ground level to escape the Earth's grav. field, then I can take E_p@infinty = 0? From that |E_k|=|E_p| to find the speed? - Kamataat

If h, the height of a body from the ground, approaches infinity, then the body's potential energy approaches 0? I'm assuming a non-constant value for g. E_p = mgh. In this equation I get 0 times infinity, which is mathematically indeterminate, but I'm guessing that the physical interpretation...