Suppose P([0,∞)) = 1. Prove that there is some n such that P([0,n]) > 0.9

I cant figure this out.

(Wondering)

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- Jun 22nd 2011, 11:45 AMKanwar245Continuity of P
Suppose P([0,∞)) = 1. Prove that there is some n such that P([0,n]) > 0.9

I cant figure this out.

(Wondering) - Jun 22nd 2011, 11:52 AMPlatoRe: Continuity of P
- Jun 22nd 2011, 11:55 AMKanwar245Re: Continuity of P
- Jun 22nd 2011, 12:06 PMPlatoRe: Continuity of P
- Jun 22nd 2011, 12:09 PMKanwar245Re: Continuity of P
- Jun 22nd 2011, 12:47 PMPlatoRe: Continuity of P
You are given that $\displaystyle \lim _{n \to \infty } P\left( {\left[ {0,n} \right]} \right) = 1$.

That means that $\displaystyle \left( {\exists N} \right)\left[ {n \geqslant N\, \Rightarrow \,\left| {P\left( {\left[ {0,n} \right]} \right) - 1} \right| < 0.1} \right]$.

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