Subsequences

Borg7 · Posted: Fri Nov 25, 2011 9:02 pm Post subject: Subsequences

Be (X,d) a metric space and (x_n)_n€N a sequece in X. Prove: (x_n)_n€N converges when the subsequences (x_2n)_n€N, (x_2n+1)_n€N and (x_3n)_n€N converge.

Any ideas?
_________________
"I dont believe in anything other than alians"
Dominic Heydon

aggsyb · Posted: Fri Nov 25, 2011 9:34 pm Post subject:

Yea stop trying to make yourself look so smart for ego. Your making yourself look gay

Borg7 · Posted: Fri Nov 25, 2011 9:38 pm Post subject:

Lol, I need to hand in the paper soon but idk how to solve this...it's prob pretty simple for some1 who's good at math
_________________
"I dont believe in anything other than alians"
Dominic Heydon

Brokerstar · Posted: Fri Nov 25, 2011 9:39 pm Post subject:

aggsyb · Posted: Fri Nov 25, 2011 9:41 pm Post subject:

I think the biggest problem though is that your still coming accross as gay, and its common knowledge that gay people are not liked and in some countries not tolerated. Dont go travelling

Borg7 · Posted: Fri Nov 25, 2011 9:45 pm Post subject:

chesslw · Posted: Sat Nov 26, 2011 11:33 am Post subject:

I might be able to answer this, or at least give you a hint. It really depends how much you have "proved" so far.

But if you know that any subsequence of a convergent sequence converges to the same limit (or if not then use for all epsilon there exists N etc etc it isn't too hard), then consider:

X_6n which is a subsequence of X_2n and X_3n, therefore X_2n and X_3n converges to the same limit. Similarly X_6n+3 is a subsequence of X_2n+1 and X_3n, and so X_2n+1 and X_3n have the same limit.

Therefore all 3 sequences have the same limit, x say, so the whole sequence converges to the same limit.

Of course you should use formal notation, i.e. epsilon-N notation.

Hope that helps!

Edit- missed the v. important bolded part the first time...

BetMagicMoney · Posted: Sat Nov 26, 2011 11:44 am Post subject:

feck knows, i like to think i know math but this is just some high level sh1t bro Razz

_________________
"When everything seems to be going against you, remember that the airplane takes off against the wind, not with it."
Borg7

"Lol he'll get there tho. He is a smart guy"
_red_dog

follow me on twitter @BetMagicMoney

aggsyb · Posted: Sat Nov 26, 2011 12:05 pm Post subject:

U Cook Socks · Posted: Sat Nov 26, 2011 12:16 pm Post subject:

	Tagpoker Forum Forum Index -> Tagpoker Lounge	All times are GMT Page 1, 2, 3 Next
Page 1 of 3