Recent content by nikkor180

Greetings: I watched several videos describing so-called "empty space" as being permeated with fields (electron field, quark field, etc.). Is it possible that it is actually these fields that curve about large masses and that the trajectory of light and matter curve because they follow the...

Greetings: I hope I am posting in the appropriate forum. I understand that in special relativity, Einstein expressed e = mc^2 as m = e/c^2. Is this his way of defining mass? If not, can you explain how he came to this conclusion?

Greetings: I can understand that an object's trajectory curves about a greater mass (e. g., satellite in Earth's orbit). The spacetime is curved via the great mass and the moving object simply follows the curvature. My problem is this: Why does a stationary object at a short distance from...

Deveno: Thank you so much for responding to my post. That was quite a nice dissertation! Best wishes, Rich

In English grammar, we typically refer to specific branches of mathematics without a prefixed article; e.g., solve using algebra, trig., etc.. By contrast, we often prefix calculus with the definite article, "the". For instance, "solve via the calculus". Can anyone explain this exception to...

Thanks folks.

Evgeny.Makarov: Thank you for responding to my post. 1) I mean "S is an element of S" (not subset). Regarding "If X is in S for some X not=S, then S - S cannot be empty", I need to ponder that further. I will respond soon. Thanks again, Rich B. BTW, can you tell me how to access symbols...

Greetings: I am attempting to prove that no set contains all sets without Russell's paradox. What I have thus far is this: Let S be an arbitrary set and suppose S contains S. If X is in S for some X not=S, then S - S cannot be empty. But this is a contradiction; hence if S contains S, then...

Greetings: If you let u = tan(x/2), then dx = 2*du /(u^2+1), sin(x) = 2u/(u^2+1), cos(x) = (1-u^2)/(1+u^2). If you substitute these values appropriately, each integral should return an inverse trig function. Regards, Rich B.

Greetings: d/dx [ln(x)] = lim(h-->0) [(ln(x+h) - ln(x)) / h] = lim(h-->0) [(1/h)*ln[(x+h)/x] = (1/x) lim(h-->0) [(x/h) ln(1+h/x)] = (1/x) lim(h-->0) [ln(1+h/x)^(x/h)] = (1/x) ln [lim(h-->0) [(1+(h/x))^(x/h)]] {from lim[f(g(x))] = f(lim[g(x)])} = (1/x) ln e = 1/x. Since...

Greetings: I believe the point of interest to be none other than the center of mass which is at mer / (me + mm) meters from the Earth along the ray extending from Earth through the moon. Regards, Rich B. rmath4u2@aol.com

Greetings: If acceleration due to gravity is equal for both the Earth and another planet, then, Gme / re2 = Gmp / rp2. ==> me = (re / rp)2 mp ==> me = (2rp / rp)2 (given re = 2rp) ==> me = 4mp Regards, Rich B. rmath4u2@aol.com

Greetings: The previous poster was indeed correct in that the numerator's second term goes to zero. That said, the limit becomes, limit(x-->inf) [(ln(1 + 1/sqrt(2))^x) / x]. From the property log(u^n) = n*log(u), we have, limit [x*ln(1 + 1/sqrt(2)) / x] = limit [ln(1 + 1/sqrt(2))] =...