I'm reading Homer and Selman's "Computability and Complexity" book. In some Corollary 5.3 it says:
For all ε > 0, DTIME(O(n)) = DTIME( (1+ε) n).
Now I'm confused with this corollary and Rosenberg's result (p87 in the same book):
DTIME(n) ≠ DTIME(2n).
Why can we not use the corollary to show that DTIME(n) = DTIME(2n)?