Borg7
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SubsequencesBe (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?
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aggsyb
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Yea stop trying to make yourself look so smart for ego. Your making yourself look gay
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Borg7
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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
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Brokerstar
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| Borg7 wrote: | | 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 |
'good at math' or math genius?
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aggsyb
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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
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Borg7
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| Brokerstar wrote: |
'good at math' or math genius? |
do you remember the sn of the mathematician guy on here?
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chesslw
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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...
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BetMagicMoney
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feck knows, i like to think i know math but this is just some high level sh1t bro 
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aggsyb
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| chesslw wrote: | 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... |
So hold on a sec, what your saying is it has NOTHING to do with being like and or actually being gay?
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U Cook Socks
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| aggsyb wrote: | | chesslw wrote: | 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... |
So hold on a sec, what your saying is it has NOTHING to do with being like and or actually being gay? |
I'm fairly certain it does to be honest.
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chesslw
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| aggsyb wrote: | | chesslw wrote: | 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... |
So hold on a sec, what your saying is it has NOTHING to do with being like and or actually being gay? |
lol. Where did I say THAT in the reply?
I, in fact, agree with you- that metric/topological spaces are a bit gay. From what I remembered it was all this talk about balls of radius epsilon around each other- and it's not useful in any shape or form for real life except a few bad jokes to share with other "gay" ppl.
Or is this thread a big level?
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BetMagicMoney
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| chesslw wrote: | | aggsyb wrote: | | chesslw wrote: | 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... |
So hold on a sec, what your saying is it has NOTHING to do with being like and or actually being gay? |
lol. Where did I say THAT in the reply?
I, in fact, agree with you- that metric/topological spaces are a bit gay. From what I remembered it was all this talk about balls of radius epsilon around each other- and it's not useful in any shape or form for real life except a few bad jokes to share with other "gay" ppl.
Or is this thread a big level? |
whats leveling??
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Brokerstar
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| BetMagicMoney wrote: |
whats leveling?? |
Seriously man you've been a member of this site for ages now and you still don't know what a level is?
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chesslw
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Joking/leveling aside- what I said should be the correct answer...
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BetMagicMoney
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| Brokerstar wrote: | | BetMagicMoney wrote: |
whats leveling?? |
Seriously man you've been a member of this site for ages now and you still don't know what a level is? |
bro i just owed you so hard 
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Borg7
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| chesslw wrote: | 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... |
THANK YOU 
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U Cook Socks
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| Borg7 wrote: | | chesslw wrote: | 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... |
THANK YOU |
Does this mean you are in a relationship now ?
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BetMagicMoney
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| Blazing_Saddler wrote: | | Borg7 wrote: | | chesslw wrote: | 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... |
THANK YOU |
Does this mean you are in a relationship now ? |
yes 
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Brokerstar
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| BetMagicMoney wrote: |
bro i just owed you so hard |
At leveling? Are you sure?
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chesslw
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| Brokerstar wrote: | | BetMagicMoney wrote: |
bro i just owed you so hard |
At leveling? Are you sure? |
One of you has just got leveled... though I'm not sure who (and I'm not even sure if either you know too).
Or maybe I've got leveled??? 
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chesslw
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| Borg7 wrote: | | chesslw wrote: | 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... |
THANK YOU |
No problem... I thought I heard you did physics???
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forced
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| Brokerstar wrote: | | BetMagicMoney wrote: |
bro i just owed you so hard |
At leveling? Are you sure? |
Im still trying to figure out how much he owed you...
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BetMagicMoney
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| Brokerstar wrote: | | BetMagicMoney wrote: |
bro i just owed you so hard |
At leveling? Are you sure? |
but are you sure?
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chesslw
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| forced wrote: | | Brokerstar wrote: | | BetMagicMoney wrote: |
bro i just owed you so hard |
At leveling? Are you sure? |
Im still trying to figure out how much he owed you... |
lololol forced I didn't even notice that
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Borg7
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chesslw, the solution you posted was actually almost completely correct (except for the notation obv), ty again.
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forced
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| chesslw wrote: | | forced wrote: | | Brokerstar wrote: | | BetMagicMoney wrote: |
bro i just owed you so hard |
At leveling? Are you sure? |
Im still trying to figure out how much he owed you... |
lololol forced I didn't even notice that |
lol... I thought it was fitting...
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chesslw
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| Borg7 wrote: | | chesslw, the solution you posted was actually almost completely correct (except for the notation obv), ty again. |
No problem- if you have any pure maths related questions (though no logic theory) then you can ask me.
In all these questions there is always a small trick- e.g. here you need to consider X_6n and X_6n+3, and then of course write down the answer formally (given epsilon, choosing some N s.t. for all n>N, X_n < epsilon blah blah blah). Once you have done a few, you will be able to develop intuition for these tricks just like in poker.
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