I am trying to reconcile the following statement:(adsbygoogle = window.adsbygoogle || []).push({});

" ||u||<=eps*||f|| means ||u||=O(eps) ("||u|| is order eps")... "

with the limit definition of "big O"; considering it's not clear that ||u|| here even depends on eps:

" lim as eps goes to 0 of ||u||/eps, by definition of "big O", should equal some constant "; is it necessarily ||f||?

I understand that, for example, sin(x)=O(x) because lim as x goes to 0 of sin(x)/x is bounded.

So to casually say something is "order epsilon", if it doesn't depend on epsilon, I am not sure how to reconcile that with the definition of "big O" given by the limit one should be able to take, as above.

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# Big O notation question

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