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I ask this because of this:

2n² O(n²) means that 2n² <= c*n² which it is true for c=3 and n>=1 for example

Instead, it would be like this:

c*2n² <= n² which would be true for c=1/3 and n>=1 for example

and in the Ω case, 2n² Ω n² means that c*2n² <= n² ,which is true to c=1/3 and n>=1 for example. Instead could it be defined so it would means that 2n² < c*n², which would be true for for c=3 and n>=1, for example. Basically changing the meaning of these notations

The same would be applicable to o and ω notations.

And in the case of n²-2n = θ(n²), instead of c1*n²<=n²-2n<=c2*n² could it be c1*n²-2n<=n²<=c2*n²-2n adjusting the coefficients as needed?

It is all of this valid, or there is some restriction that forces these definitions to be that way?