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Example question

Prove that $ exp(n) = e^{n} \space \space \forall \space n \in \mathbb{Z} $

First I prove by induction for $ n \geq 0 $ and then I do the same for $ n \leq 0 $

Is this allowed ?

Gregory Peck
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    Yes but what are your definitions of $e^n$ and $\exp(n)$? This seems very odd. – AlexR Feb 11 '15 at 15:10
  • It seemed very odd to me too, but it's based on what we have proved in our lecture notes thus far. The use of "backward induction" was my main question. Thanks for the answer. – Gregory Peck Feb 11 '15 at 15:16

1 Answers1

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Yes. If you have a proposition $P(n)$ for $n<0$, consider $Q(n)=P(-n)$, for $n>0$.
If you can prove $Q$ by induction, then you have proved $P$.

lhf
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