I was asked to prove, every punctured open set in R^2 is path connected.
My argument : take points x and y. let z be the point we've taken off from U (open).
if x, y,z do not pass through a staright line, we have a segment between a and y.
Now if the 3, i.e. x,y,z lie on a straight...
We had a series of 4 lectures by Prof. Langlands as well(possibly, he's touring India)...the topic being "Probabilistic Statistical Mechanics".
I just went there to get a glimpse of the legend( I attended only the first one)...
I meant f(x) is that expression and not (f(x))^-1.
But well...I just got to know that the problem can be solved not using ordinary generating functions but will require "something" called exponential generating functions.
Can Someone here please give me a motivation for the concept of...
We are about to begin this topic soon in class...
I'd like to know all about generating functions and their application. I tried reading it up...One thing I'd like to know is, once you have a generating function...then what? You get some information...but what is it?
I tried to find no. of...
Hello...I need help and I know this is a very simple problem...I don't know why I'm getting stuck( Maybe because it's past midnight here:frown: )
Assume that f is non-negative on (0,1) and the third derivative of f exists on (0,1).If f(x)=0 for at least 2 values of x in (0,1), show that there...
how do we get the inequality 1<= a1 <=.......<=a77 <= 132 ?? it hasn't been mentioned anywhere that the number of games played keeps increasing with each passing day, has it??
The reason I decided to post my queries out here is simple:I believe that ideas of PF members,by and large,represent the ideas of the world. :smile:
I've been learning indian classical music for about 12 years now...have lots of friends who're equally passionate about music.I guess...
"Temple" by Matthew Reilly is a good choice for sci-fi buffs..."The Da Vinci Code" was superb too...
but if you've just begun reading...don't miss "Sherlock Holmes". Holmes' indian counterpart "Feluda" (satyajit ray) is pretty good too...
in connection with the math rankings...what's the basis of these rankings?? also wouldn't the rankings vary when you look at specific areas in mathematics(pure or applied)?
here's a proof of the question i had posted....thanks to matt grime(he sent me the proof) and i guess chingkui's done the same thing...so he gets to ask the next question...
Let b be the square root of two, and suppose that the numbers
If nb mod(1) are dense in the interval [0,1), then m+nb...
By mere observation, it's quite clear that a_1 < a_2 <.......<a_n.....
so, it's an increasing sequence...
but i can't think of how we can show it's bounded...i mean,how do we use the recurrence relation?..and i guess, once we find the upper bound it would be easy to spot the limit of the...
given a recurrence relation, a_1 =2^(1/2) and a_n = (2 +a_n-1)^1/2 ...prove that the sequence converges and find its limit..
are we supposed to begin by guessing the limit and the bounds ??
i think i don't have adequate theory to solve these problems.... :frown:
1.given that f(x) =cos(x) sin^k(x) / (1+x). calculate integral of this function wrt x between limits 0 and pi/2 . then find the it's limit as k tends to infinity...
2.let f(x)={e^(-ax)-e^(-bx)}/x, 0< a< b .let I be...
why not do something simpler? all you need to do is to find the point Q on the line where the normal vector passing through (3,-2,4) cuts it...that point looks like (1+t,4-3t,-2+2t) for some t. that is the t you need to find...and to do that use the fact that PQ is normal to the given...
i know it's a bad idea but looks like this is gonna be the end of this sticky... :grumpy:
anyways...i want to work on the problem i posted....chingkui,could you elaborate the circle part...didn't quite get that...
may be you could start by finding a one-one, onto map from [0,1] to [0,1] (cross) [0,1]. i mean a bijective map from [0,1] to the unit square in the plane.
I think spirituality is something very personal....a billion people will have a zillion different views on the subject. a person who views spirituality as a means of achieving a higher goal in life will, i think, not talk about it...but prefer to practice it in silence.
so, essentially, the...
Hi!
Here is a problem I've been struggling with,so it appears real tough to me.just for the record...i haven't (yet) been able to write down a proof for it...
prove that Z + 2^(1/2)Z is dense in R.
(in words the given set is the set of integers + (square root of 2) times the set of...