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If we have a sequence of real numbers [itex]x_{n}[/itex] converging to [itex]x[/itex], that means [itex]\forall \epsilon > 0, \exists N [/itex] such that [itex] |x_n - x| < \epsilon, \forall n \geq N.[/itex]

So, can we say [itex] P (|x_n - x| < \epsilon \ i.o.) = 1[/itex] because for [itex]n \geq N[/itex], [itex] |x_n - x| < \epsilon [/itex] always holds?

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# Limit definition and infinitely often

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