What should be range of unique frequency?

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Mohsinshaikh

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Hi, All
I am a Learning DSP.

I have one doubt,

According to Prokias : Range of unique discrete frequency for sinusoids is
-1/2≤f≤1/2 f=F/fs cycles/sample

But sinusoids with f = -1/2 and 1/2 are identical.

then how they can be distinct , Is there any printing mistake in book.

According to me range of unique frequencies should be -1/2<f≤1/2
ie (-1/2,1/2] or [-1/2,1/2) am I right ?

Also for f = 1/2 (nyquist sampling) pure sine wave have all zero samples , then how it can have maximum rate of oscillation?
 

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