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Help with a question: Prove a contaant sequence in R^p is convergest to the constant

  1. Oct 18, 2007 #1
    prove [tex] \ A_n = ( a, a,a,a,a,...) [/tex] converges to zero. [tex] a \in \ R^p [/tex]

    Been reading this real analysis book before i take it next semester and been a lil stuck on this question. Im probably making it seem more difficult than it is. Most of the questions had examples in the chapter but this one didnt. can some one help me out?
     
  2. jcsd
  3. Oct 19, 2007 #2
    If A_n = (1_1,1_2,...1_p) then A_n is constantly point with coordinates 1. This An will NOT converge to 1, it will converge to the constant itself.

    i think you are confusing a point in R^p with the sequence itself a point in R^p is a set of p real numbers where the order in which each of these numbers follow each other matters.
    a itself is NOT a point in R^p.
     
  4. Oct 19, 2007 #3
    it says that the a's are vectors in [tex] a \in \ R^p [/tex]

    would it be that same
     
  5. Oct 19, 2007 #4
    sorry, that's correct. the a's ARE vectors. sorry i thought you thought they were coordinates of the vectors in the sequence.

    well use the distance function u have and choose N=1 for any epsilon. see what happens.
     
  6. Oct 19, 2007 #5

    HallsofIvy

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    First, as the sticky at the top of this section says, this is NOT the place for homework. I am moving it to the homework section.

    Second, you misstated the problem in the body of your post. You do NOT want to prove "that (a, a, a, a, ...) converges to 0" because, in general, it doesn't. You want to prove that it converges to a. Okay what is |a- a|?
     
  7. Oct 19, 2007 #6
    ^^^ yes thats what i meant
     
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