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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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