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ak123456
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1. Homework Statement [/b]
Let Jn : n [tex]\in[/tex]N be a sequence of intervals Jn=[tex]\left[[/tex]an,bn[tex]\right][/tex] such that J1[tex]\supset[/tex]J2[tex]\supset[/tex]...[tex]\supset[/tex]Jn[tex]\supset[/tex]Jn+1[tex]\supset[/tex]...
suppose also that the sequence xn=an-bn converges to 0 as n tends to infinite.Show that there is exactly one point a such that a[tex]\in[/tex]Jn for all n [tex]\in[/tex]N
i don't know how to start it , any clue??
Let Jn : n [tex]\in[/tex]N be a sequence of intervals Jn=[tex]\left[[/tex]an,bn[tex]\right][/tex] such that J1[tex]\supset[/tex]J2[tex]\supset[/tex]...[tex]\supset[/tex]Jn[tex]\supset[/tex]Jn+1[tex]\supset[/tex]...
suppose also that the sequence xn=an-bn converges to 0 as n tends to infinite.Show that there is exactly one point a such that a[tex]\in[/tex]Jn for all n [tex]\in[/tex]N
Homework Equations
The Attempt at a Solution
i don't know how to start it , any clue??