Suppose you are building a sequence consisting of 0 and 1 in such a way that:(adsbygoogle = window.adsbygoogle || []).push({});

- you start with 1

- no consecutive 0s are allowed

Examples of such sequences are: 1, 1010, 110111101 etc. Empty sequence is also allowed.

I want to prove by induction that the number of 0s in such a sequence is never greater than the number of 1s.

(Btw, I managed to prove that the length of such a sequence is at least the number of 1s inside, but I am not sure that the proof for this is any similar to this one.)

I tried almost every form of induction I could think of (except nested induction), but simply couldn't prove it. Please help.

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# Stuck with a simple induction problem

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