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ptolema
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Homework Statement
suppose that {an} is a convergent sequence of points all in [0,1]. prove that lim an as n-->[tex]\infty[/tex] is also in [0,1]
Homework Equations
for all[tex]\epsilon[/tex]>0, [tex]\exists[/tex] a natural number N such that for all natural numbers n, if n>N, then absolute value(an-L)<[tex]\epsilon[/tex]
The Attempt at a Solution
i messed with the limit a lot, but the furthest i could get was that [0,1] was a subset of (-[tex]\epsilon[/tex],1+[tex]\epsilon[/tex]), which contains L (the limit). can someone shed some light on this?