Recent content by adityab88

Firstly, I strongly suggest you study topology. You won't be able to understand such concepts without knowledge of that course, and it is a crucial course in your study of mathematics. Just read any introductory book. Your question is very basic (I think it will also be answered in a standard...

Let u,v be in U⊥. Let k be a constant in R. Now <u,w>=0 for all w in U and <v,w>=0 for all w in U. Thus by linearity of inner product we have <u+kv,w>=0 for all w in U. Thus, u+kv is also in U⊥ for all u,v,k. Thus U⊥ is a subspace. For the second part, DIY but here are some hints: - We...

We know that a linear operator T:X\rightarrowY between two Banach Spaces X and Y is an open mapping if T is surjective. Here open mapping means that T sends open subsets of X to open subsets of Y. Prove that if T is an open mapping between two Banach Spaces then it is not necessarily a closed...

good stuff good stuff how long did it take you to "experiment" and find the final sequence? cause i was looking for it, too, but my experimentation did not really work.

hello ... ppl i am quite sure you do not need programming equipment. just your brains will suffice; i am sure of this because i saw this question on a maths paper, where computers were not allowedthis is all i have: the difference between the consecutive primes has to be a multiple of 30, i have...

dedekind cuts/ cauchy sequences precisely. dedekind cuts or even cauchy sequences can be used prove such a statement.

just read a number theory book i am sorry in that i did not mean it to come that way. all i mean is that an answer to such a question is pretty standard and can be found in almost any number theory textbook. people can just read up the solutions. i did not mean to humiliate ppl. sorry...

this is not number theory this is not number theory, but it is instead mathematical analysis. it is a very basic result that has been used to construct the real numbers and i think you will find it in any standard intro to analysis textbook (i personally recommend principles of mathematical...

Find the smallest possible arithmetic sequence consisting of seven primes. For example, the smallest possible arithmetic sequence consisting of five primes is: 5, 11, 17, 23, 29. By the way, by "smallest possible" I mean that the last term in the sequence must be the smallest possible of...

it's quite easy prove by contradiction i am very suprised that such an EASY question has stumbled so many of you people. you should be ashamed of yourselves