I am 16 years old at the time of writing (so I have no supervisors to seek advice from) and I have written a mathematics research paper, which I plan on submitting to a journal for publication. I asked an identical question on Academia.SE and I was advised to ask the question here.

For a couple of the assertions that I make, I use proofs by induction. Now, in school we're encouraged to write proofs by induction in the following (rigid) format:

**Base case:**...

**Assumption(s):** ….

**Inductive step:** ….

**Conclusion:** ….

I have noticed that no research articles that I have seen have written proofs by induction using this sort of format. The authors usually make it flow much more smoothly, eg 'For the base case, the result is trivial. Now assume the result holds for some $n=k$, so that …. Now consider the expression for $n=k+1$ … and by the inductive hypothesis this equals … hence the result is true by mathematical induction.'

So, is it good practice to write proofs by induction in the pretty rigid structure I first outlined or is it ok/better to write the proofs more naturally so that it flows better?

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