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This is a snapshot from coreman.

Here if i want to prove this example

$2n^2$ = $o(n^2)$

And if i take c=3,

then

$2n^2$ < $3n^2$

Now for all n0 and c=3 it will hold and this will be true .I know this proof i gave is wrong.But  what exactly is  wrong ?

main thing to focus is a word-> for any positive constant c

it means, it should hold for all the positive value of 'c', not only for few.

The description says "any positive c" and a fixed "$n_0$" but you took the reverse.
Thanks.i confused with big o,which says "there exists positive constant c",but here it is "any positive c"
@Arjun sir,

is it correct to say that if a bound is not tightest upper bound, than that bound will always be small-Oh (o) ?

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