- #1
ericm1234
- 73
- 2
I am trying to reconcile the following statement:
" ||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.
" ||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.