#math definitions

The inverse and reciprocal are not the same thing. An inverse is a function that will take that output of f(x) and give you x. A reciprocal is an expression that is taken to the first negative power. An inverse must be a function. The period isn’t a function in most cases and when it is it’s probably 2pi times the wave number. This means T(w) = 2pi/w. We can also define frequencies this way; F(w) = 2pi*w. If we input F into T we get T(F(w)) = 2pi/(2pi*w) or 1/w this is not w and thus Frequency is not the inverse of period. It is the reciprocal.

you know it's time to sleep when the smut you're reading starts to mix with series definitions of all things before your mind's eye