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This pertains to an explanation of Big-O notation:

If one pair of witnesses is found, then there are infinitely many pairs. We can always make the k or the C larger and still maintain the inequality f(x) <= Cg(x)

Any pair C' and k' where C < k' and k < k' is also a pair of witnesses since whenever x > k̍ > k.

What does that apostrophe character about the Cs and Ks mean exactly?

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  • $\begingroup$ It means they're completely different entities, different variables. $\endgroup$
    – BrianO
    Feb 15, 2016 at 3:46

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It means other constants (than $C$ and $k$, respectively), but playing the same role. You can replace $C^\prime$ by $D$ and $k^\prime$ by $\ell$ if you prefer.

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