Why the Nyquist frequency is 0.5 of Fs, why not 0.55 or 0.65?, brief explanation
From the definition of sampling, and the definition of periodicity follows that any signal is identical to signal at a frequency higher by an integer amount of sampling frequencies.
Since for real signals, negative frequencies aren't distinguishable from positive ones, it directly follows that for every $0.5f_\text{sample}\le f \le f_\text{sample}$, there is a negative frequency $-0.5f_\text{sample}\ge \tilde f=1- f \ge f_\text{sample}$ that looks the same as a positive frequency.
Hence, only frequencies lower than $|f| &lt; 0.5f_\text{sample}$ can be uniquely represented.