Digital low pass filter vs continuous low pass filter,?
A discrete spectrum has a unique span extending from $-f_s/2$ to $+f_s/2$ where $f_s$ is the sampling rate (this is referred to as the first Nyquist Zone in the analog domain), thus in terms of normalized frequency when we divide the analog frequency by the sampling rate, it extends from $-0.5$ to $+0.5$ or $\pi$ to $\pi$ depending on which units we use as described further below. 

In the case of a discrete implementation, the unique spectrum extends from $-\pi$ to $+\pi$ radians/sample. This is a common unit of frequency for sampled systems while cycles/sample is also used, which extends from $-.5$ to $+0.5$. The discrete frequency spectrum is periodic beyond these boundaries, so there is no reason to include them as no further information will be provided. 

These units are the units of "normalized frequency" as they are arrived at by dividing the analog frequency units (either cycles/second or radians/second) by the sampling rate $f_s$. Cycles/Sec is equivalent to Hertz. The sampling rate is in units of samples/second therefore we get:

Normalized frequency:    Cycles/Sec / Samples/Sec = Cycles/ Sample.

Normalized Angular Frequency: Radians/Sec/ Samples/Sec = Radians/ Sample.

That said, the passband of a discrete low pass filter must extend to an amount less the $\pi$ (in radians/sample units) since $\pi$ represents the highest frequency of the discrete spectrum.