# What does the frequency band mean when it comes to finding aliases?

The time signal which i'm trying to find the aliases for is:

$$x:{\mathbb R}\rightarrow {\mathbb R}\\\ x(t)=\cos(50t) +2\cos(70t).$$

If the sample period is $$T_s = \frac{\pi}{60}$$ then according to Nyquist -Shannon sampling theorem (which btw my professor failed to prove) there is/are a signal(s) which after sampling will be equal to the sampled version of the above signal, if we sample those with the same sample frequency in the frequency band $$[-55, 55]$$.

I don't understand the meaning of the last sentence , what does a frequency band means here?