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Math Help - analysis question

  1. #1
    Junior Member
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    analysis question

    1. For some ε > 0 there exists an index N such that
    if n > N then absolute value of an- a < ε

    2.For each ε > 0 and each index N if n > N then absolutue value an-a <ε
    3.There exists an index N such that for all ε > 0 if n > N then absolute value an-a < ε
    4. For each ε > 0 and each index N if n > n then absolute value an-a<ε




    Match from 1-4

    a) The sequence {an} is bounded
    b) The sequence {an} is a constant
    c) All except finitely many terms of the sequence {an} are equal to constant a
    d) Such a sequence does not exist
    e) The assertion holds for every sequence
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by wvlilgurl View Post
    1. For some ε > 0 there exists an index N such that
    if n > N then absolute value of an- a < ε

    2.For each ε > 0 and each index N if n > N then absolutue value an-a <ε
    3.There exists an index N such that for all ε > 0 if n > N then absolute value an-a < ε
    4. For each ε > 0 and each index N if n > N then absolute value an-a<ε
    4. The sequence is constant since we may let N=1, then it asserts that for all \varepsilon>0 :|a_n-a|<\varepsilon, which implies that for all n\ge1:\ a_n=a.

    CB
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