hmm?
hmm?
Theorem: If {s1, s2, s3, ...} converges to S and {t1, t2, t3, ...} converges to T, then {(s1+t1), (s2+t2), (s3+t3), ...} converges to S + T.
Proof:. Choose ∂ > 0. Since {sn} -> S, there exists an integer N1 such that |sn - S| N1. Since {tn} -> T, there exists an integer N2 such that |tn - T| N2. Hence, if N = max{N1, N2}, then
|(sn+tn) - (S + T)| = |(sn - S) + (tn - T)| ≤ |sn - S| + |tn - T| `` ∂
whenever n ≥ N, which shows {(sn+tn)} -%% S+T.
EDIT: The forum software changed a bunch of my notation.
:(
the sum of two convergent sequences converges to the sum of the limits?
really?
pathetic
frank reynolds wrote:
the sum of two convergent sequences converges to the sum of the limits?
really?
pathetic
That's the only simple, elegant proof I remember off the top of my head.
A couple years ago I figured out where the cut off is for when you should stay or roll again on The Price Right's big wheel. Thought it was going to be quick but it was a little tough since i had to factor in the spins of the following 2 players. I believe the cutoff was 65, meaning anything higher you should keep but I'm not sure. I'll check to see if I still have it written down somewhere.
Also I make great use of my time on a daily basis...
how about exercise 5.6 in
For each positive integer n, prove that
10^10^10^n + 10^10^n + 10^n - 1
is not prime.
The four minute mile. JK, I'm bad at math and running.
How do you measure complexity?
For example: Fermat's last theorem is a simple problem to state, but Wiles' proof is really hard to understand...
maths is for nerds
k-omega model coupled with energy and continuity equation to evaluate the effectiveness of augment roughness to improve heat transfer efficiency index.
2 + 2 = 5
How much money to spend to get the girl while not being too broke to keep the girl.
I beat Might and Magic for the Genesis, deciphering the alien code at the end. Winning!
Rewrote and simplified a few equations at work for end of day production reports by backward engineering the existing ones. Trying to explain it to everyone was hilarious as they all just nodded, no one understood what I did. And I\'m far from gifted in mathematics, scary.
We can't even see Question 5.6 in preview - and you call someone else's response "pathetic?"
Consider k runners on a circular track of unit length. At t = 0, all runners are at the same position and start to run; the runners' speeds are pairwise distinct. A runner is said to be lonely at time t if he is at distance of at least 1/k from every other runner at time t. The lonely runner conjecture states that each runner is lonely at some time.
once I understood "1+1=1" I became enlightened
Numerous proofs in my Topology class in college, during the second half of the semester. Can't pick one off the top of my head. We always had to prove one difficult theorem each week in addition to our easier proofs.
If a train leaves Chicago at 1:00 going 85mph and another train leaves NYC at 2:00 going 95 mph when will they meet and in what state will they meet?