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??
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 ??
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...
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...
Ok…so I think I’ve got something (not a proof) here…
Let A be a paired set containing an irrational point, say x. 0,x,1 belong to A and x-0 != 1-x, so there exists at least one additional point which is irrational or two points,at least one of which is irrational.
In the first case, say , the...
i'm writing down the proof...i'm onto it ,head on...
but there's something i'd like to clarify...
in a paired set ,is it possible to have 3 pairs of elements having the same distance between them....or do we consider it to be exactly two pairs?
Let’s say you have an irrational x in A which is a paired set. You’re sure of 0,x and 1 being in the set. Now, obviously x-0 != 1-x .So there must be at least one additional point in the set (or two points p,q distinct from x such that p-q=x-0) .Now this point is irrational( in the other...