Recent content by sujoykroy

As far as my little brain progressed, i figured out as follows. Since the equation δ\int_P^{P'}ds=0 is evaluated between two points of four coordinates continuum, to convert this into a well-known form of variation some parametrization was required and hence λ was introduced. Using λ, all those...

I was reading "The foundation of the general theory of relativity" by Albert Einstein. I faced some difficulty to understand his derivation of "geodetic line", stated in "The equation of the geodetic line. The motion of particle" headed section. I will try to describe my problem clearly and in...

I was reading Einstein's paper "The Foundation of the General Theory of Relativity" and as i understood, he tried to establish that gravitation arises due to different kind of motions of objects. As per his opinion, in infinitesimally small space-time region special theory of relativity is still...

Which experiment does show that electron has a spin of magnitude of \frac{1}{2}\hbar? I guess, Stern–Gerlach experiment shows that electron has a kind of intrinsic spin; because of which, particle beam gets deflected in some specific way under the application of an external magnetic field...

“But what is a Turing machine? It is, indeed, a mathematically idealized computer (the theoretical forerunner of modern general-purpose computer) – idealized so that it never makes any mistake and can run on for as long as is necessary, and so that it has an unlimited storage space” - Roger...

Square of integer is quite easy, childlike stuff. But there is no harm in seeing a known thing in different lights. Experimenting on any thing is always fun, at least initially. So, while reading some stuff on semiconductor physics I came to think about viewing square of integer in different...

Agree with you to some extent. But, i don't think we should take the term "imaginary" in its literal meaning. Mathematics, more specifically Algebra, is about the playing with relationships among numbers ignoring the interpretation of the numbers. So, imaginary means which doesn't directly...

I found a falsehood in the definition of event j as moving 3 marks in 12-3-6-9-12 direction. It doesn't satisfy j2 = -1, because j2 means moving 3 * 3 =9 marks (exceeding 6 marks, the upside down condition) and j4 means 81 marks (which will never put your head at 12 mark position). If we...

I think the very first equations that intrigue the mind of early wise persons were related with physical phenomena. While providing solutions to such equations, they stumbled upon the game of playing with different possibilities of previously discovered concepts. And thus they might think about...

Can anybody give example of a physical phenomenon which can be stated into a polynomial equation (cubic, quintic or whatever) and which has complex number solutions and those complex numbers have some physical interpretation? The reason for asking such question tagged in physics is that i...

I can't remember the website. It is a .DJVU version. I was searching for a good book on set theory and landed up with it.

Page 87 of "Introduction to Set Theory" Sorry, if this post doesn't fit into this forum, but i had no other choice. I got a electronic version of "Introduction to Set Theory" by "Karel Hrbacek" and "Thomas Jech". It is a magnificent book which opens up every window of understandings of...

Thanks. Actually i was trying to understand/prove the use/existence of Infinite Sequence used in various proof of Cantor-Schroder-Bernstein i.e. if \left|X\right|\:\leq\:\left|Y\right| and \left|Y\right|\:\leq\:\left|X\right| then \left|X\right|\:=\:\left|Y\right| and current problem was a...

I think, if you pick up a binary relation f in such way that f\left(\:a\:\right)\:=\:\left(\:a\:,\:b\:) for some b\:\in\:B for all a\:\in\:A, then f will be a one-to-one function with dom\:f\:=\:A and ran\:f\:\subset\:A\:\times\:B, hence proving that...

Can you prove the following theory of cardinality for a Cartesian product, - \left|\:A\:\right|\:\leq\:\left|\:A\:\times\:B\:\right|\: if\: B\neq\phi In English, The cardinality of a set A is less than or equal to the cardinality of Cartesian product of A and a non empty set B.