Yes, that is exactly what that notation means, just as 0.1111... is not any of the numbers 0.1, 0.11,... Supremum of an increasing sequence of reals is equal t

Yes, that is exactly what that notation means, just as 0.1111... is not any of the numbers 0.1, 0.11,... Supremum of an increasing sequence of reals is equal to the limit of the sequence in all cases.