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Math Help - Converging to an absolute Value

  1. #1
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    Converging to an absolute Value

    Prove that if {a} converges to A, then {abs value(a)} converges to absolute value(A). I want to know if the converse si true(What does that even mean?).

    Here is what I have:
    epsilon>0 is arbitrary
    A-epsilon<a<A+epsilon

    Don't know where to go with the absolute value. i'm confused....
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  2. #2
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    This is really simple!
    \left| {\left| {a_n } \right| - \left| A \right|} \right| \leqslant \left| {a_n  - A} \right| < \varepsilon .

    Consider b_n = (-1)^n then \left| {b_n } \right| \to 1
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  3. #3
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    Quote Originally Posted by Plato View Post
    This is really simple!
    \left| {\left| {a_n } \right| - \left| A \right|} \right| \leqslant \left| {a_n - A} \right| < \varepsilon .
    Ok, so then I would take off the absolute values and find n>N, right?
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  4. #4
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    Also, what does it mean when it asks if the converse is true?
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  5. #5
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    Quote Originally Posted by kathrynmath View Post
    Also, what does it mean when it asks if the converse is true?
    Does that mean if {absolute value(a)} converges to absolute value(A) then {a} converges to A?
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  6. #6
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    Quote Originally Posted by kathrynmath View Post
    Does that mean if {absolute value(a)} converges to absolute value(A) then {a} converges to A?
    yes
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  7. #7
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    Quote Originally Posted by kathrynmath View Post
    Does that mean if {absolute value(a)} converges to absolute value(A) then {a} converges to A?
    No it does not mean that.
    Consider: b_n  = \left( { - 1} \right)^n  \Rightarrow \quad \left( {\left| {b_n } \right|} \right) \to 1\,\& \,\left( {b_n } \right) \to ?
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  8. #8
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    Quote Originally Posted by kathrynmath View Post
    Does that mean if {absolute value(a)} converges to absolute value(A) then {a} converges to A?
    Quote Originally Posted by Jhevon View Post
    yes
    Come on you know better than that. It is not true.
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  9. #9
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Plato View Post
    Come on you know better than that. It is not true.
    i thought post #5 refered to post #4 which was talking about the problem in post #1

    in which case the answer is yes. asking if the converse is true is the same as asking what post #5 said
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  10. #10
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    Quote Originally Posted by Jhevon View Post
    i thought post #5 refered to post #4 which was talking about the problem in post #1

    in which case the answer is yes. asking if the converse is true is the same as asking what post #5 said
    yeah, that's what I meant.
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  11. #11
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kathrynmath View Post
    yeah, that's what I meant.
    yes, that's what i assumed you meant

    i was answering your question as to what you need to prove (or in this case, disprove) not answering the actual problem, Plato did that, and gave a nice counter example
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  12. #12
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    Quote Originally Posted by Jhevon View Post
    i thought post #5 refered to post #4 which was talking about the problem in post #1
    in which case the answer is yes. asking if the converse is true is the same as asking what post #5 said
    All I can ask is: "Did you read the posting?"
    Quote Originally Posted by kathrynmath View Post
    Does that mean if {absolute value(a)} converges to absolute value(A) then {a} converges to A?
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  13. #13
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    Quote Originally Posted by Plato View Post
    All I can ask is: "Did you read the posting?"
    yes, i did. i read it having post #4 in mind, i assumed the poster's question related to that, which the poster confirmed was correct
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