[snip phase vs inversion discussion]
Admittedly, with a sine wave, they LOOK exactly the same; this is
probably the confusion factor for those who don't know the difference
yet.
All time based signals can be expressed as a sum of sine waves. By
superposition, each of those sin waves have been inverted by your inverter,
and so they each 'look' like they are all individually 180 degrees out of
phase... are they?
The concept of phase only applies to a single frequency. But, inverting a
signal appears to change the phase of all components by 180 degrees...
Turns out that there is an old psychology experiment, in which folks went
around wearing glasses that made everything look like it was upside-down.
After a few days, they got used to it, and everything looked right-side-up
with the glasses on, whereas when they took the glasses off, everything was
upside down. So, the question is, are you currently seeing things right side
up or upside down?
Are your glasses half-full? or half empty? Which end of the egg should be
opened first? Are you a big-endian, or a little-endian?
Pick your sides now. It is important to make sure you are on the right (or
would that be the left?) side.