In amplitude modulation when carrier signal and base band signals are mixed, side band frequencies are generated. Upper side band frequency is $f_c+f_m$ and lower side band frequency is $f_c-f_m$. Wikipedia defines sideband frequencies as follows:
In radio communications, a sideband is a band of frequencies higher than or lower than the carrier frequency containing power as a result of the modulation process.
My doubt is why the definition says band of frequencies when there are only two other specific frequencies (one is upper side band frequency i.e. $f_c+f_m$ and the other one is lower side band frequency $f_c-f_m$).