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Homework Statement
Prove by induction that the set [tex] [a_{n} | n_{0}\leq n \leq n_{1}][/tex] is bounded.
[tex]a_{n}[/tex] are the elements of the sequence [tex](a_{n})[/tex]
[tex]n \in N[/tex]
Homework Equations
Definition of set bounded above:
[tex] \forall x \in S, \exists M \in R[/tex] such that [tex]x \leq M[/tex]
The Attempt at a Solution
Just proving its bounded above here...
Base step: [tex][a_{1}][/tex] The set has only 1 element and
[tex]a_{1} \leq a_{1} +1[/tex]
Now assume true for [tex]a_{n}[/tex]
[tex] [a_{n}|n_{0}\leq n \leq n_{1}][/tex]
and [tex] \exists M \in R[/tex] such that [tex]a_{n} \leq M,
forall a_{n}[/tex]
For [tex] [a_{n+1}|n_{0} \leq n+1 \leq n_{1} ][/tex]
... well I'm not really sure what to do here. Normally you use the assumption to prove it true for n+1, but I'm not sure how to incorporate the assumption here.
Please help
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