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Math Help - Continuity of P

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    Junior Member Kanwar245's Avatar
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    Continuity of P

    Suppose P([0,∞)) = 1. Prove that there is some n such that P([0,n]) > 0.9
    I cant figure this out.
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    Re: Continuity of P

    Quote Originally Posted by Kanwar245 View Post
    Suppose P([0,∞)) = 1. Prove that there is some n such that P([0,n]) > 0.9
    What is this limit \lim _{n \to \infty } P\left( {\left[ {0,n} \right]} \right) = ?.
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    Junior Member Kanwar245's Avatar
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    Re: Continuity of P

    Quote Originally Posted by plato View Post
    what is this limit \lim _{n \to \infty } p\left( {\left[ {0,n} \right]} \right) = ?.
    p([0,∞))
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    Re: Continuity of P

    Quote Originally Posted by Kanwar245 View Post
    p([0,∞))
    Do you understand the theory of limits?
    This question is based on the definition of a limit.
    In the definition use L=1~\&~\epsilon=0.1
    If you don't know what that is all about, then you should not been asked to work this question.
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    Junior Member Kanwar245's Avatar
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    Re: Continuity of P

    Quote Originally Posted by Plato View Post
    Do you understand the theory of limits?
    This question is based on the definition of a limit.
    In the definition use L=1~\&~\epsilon=0.1
    If you don't know what that is all about, then you should not been asked to work this question.
    i see i do know epsilon delta definition of a limit, but the way they proved it is with contradiction
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    Re: Continuity of P

    Quote Originally Posted by Kanwar245 View Post
    i see i do know epsilon delta definition of a limit, but the way they proved it is with contradiction
    You are given that \lim _{n \to \infty } P\left( {\left[ {0,n} \right]} \right) = 1.
    That means that \left( {\exists N} \right)\left[ {n \geqslant N\, \Rightarrow \,\left| {P\left( {\left[ {0,n} \right]} \right) - 1} \right| < 0.1} \right].

    From there 1 - 0.1 < P\left( {\left[ {0,N} \right]} \right).
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