Canonical - Greedy algorithm always yields the optimal solution.
My Thinking
Base Case:
Consider the set {$c^i:c\ge 1,i=0,...,k$} where we have $k=0$, then we get the set {$1$}
This is clearly canonical.
Hypothesis:
Suppose for some $s$, we have that {$c^i:c\ge 1,i=0,...,s$} is canonical.
WTS: {$c^i:c\ge 1,i=0,...,s+1$} is also canonical.
Step:
I don't really know how to use the hypothesis to prove this. How can I use the fact that {$c^i:c\ge 1,i=0,...,s$} is canonical to prove that {$c^i:c\ge 1,i=0,...,s+1$} is also canonical?