I have seen different type of induction proofs on this case, but trying an alternative approach I tried Induction to show that ${n\choose k}$ in binomial coefficient is an integer, where both n and k are non-negative integers.
Base case: For k = 0, ${n\choose 0}$ = 1, and is integer.
Inductive Hypothesis: For k= n-1, Assume ${n\choose n-1}$ is integer. (That's not even assumption but a fact, in fact.)
Finally, induction: For k = n, ${n\choose n}$ is integer because it's 1.
Is this a proof? Is this a thing? What is it?
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