Mach number Question
Hi, i just have a question about the mach number. I have been told that an aircraft can not fly at Mach 1 at low levels. i am now reading the"Aeroplane performance,planning &loading for the Air transport Pilot(B727) from trevor Thom" book which i bought a while ago. now i am no airline pilot but just a student pilot but what i dont understand is that the book says that Mach number =
true airspeed
---------------
local speed of sound
It also says "the higher the temperature,the faster the speed of sound.conversely,the lower the temperature,(or higer the altitude) the slower the speed of sound". now my question is: if the temperature lowers as we get higher, than why are aircraft that do speed of sound, flying at such high levels. would this not make speed of travel possible at lower levels due to the higher temps? Please dont forget that i am a student pilot!
thanks