Recent content by ShengyaoLiang

thanks...hehe i did wrong...

If ∑ C An (n from 1 to infinity) converges, and C in Real, then ∑ C An is convergent with : ∑ C An =C ∑ An (n from 1 to infinity) .. why?

anyway...i am sorry...

things i did: 1) if An converges to a, i can show that Bn converges to a , also. similarly, if Bn converges to b, i can show An converges to b , also. therefore, An converges iff Bn converges. and, obveriously, a=b 2) suppose Xn converges to a and let C = [m,n] then...

i know how to prove : Let (Xn)be a sequence converging to a and to b. then a=b... Is the prove above is similar as 1) ?

triangle inequality： ︱a+b︱≤︱a︱+︱b︱ and ︱︱a︱-︱b︱︱≤︱a - b︱

anyway, after looking the class notes ,i still have no idea... this is tooooo difficult for me.

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two question on analysis... 1）Prove : Let (An) amd (Bn) be sequences in a metric space S such that d (An , Bn) → 0. Then (An) converges if and only if (Bn) converges, and if they converge, they have the same limit. 2）Prove: Let C be a closed set and let (Xn) be a sequence in C converging to a...

i have no idea on how it works... i am learning by myself right now...so could some one help me out?...thank you very much...

The set A={1/n : n in N} is not compact. A) prove this by explicitly finding a family of open sets which covers A but has no finite subfamily whcih also covers A. B) Find another family of open sets which covers A and does have a finite subfamily which cobers A.

don't have a formal texeboot for analysis1, only have a courseware... thanks a lot.

a. 1/n + 1/m : m and n are both in N b. x in irrational #s : x ≤ root 2 ∪ N c. the straight line L through 2points a and b in R^n. for part c. i got: intA= empty ; bdA=clA=accA=L Is this correct? how about part a and part b...i am so confused...

Thank You Very Much~~~~hoho

1) give an example of a sequence (An) of open sets such that the intersetion ∩ An is not open. n in N 2) If A is a nonempty set of real numbers bounded below with no minumum, then infA is an accumulation point of A. Could somebody gives some hint on...