Does "dreamless sleep" even exist?

[Noneguy]

We know that...
We can dream in all 5 stages of sleep (not just REM)
We move around very often throughout the night (all in nREM since you're paralyzed in REM)
Memories are sorted out constantly in all stages of sleep.
Also this http://www.goertzel.org/dynapsyc/2005/ZhangDreams.htm
And if you look at history of sleep "research"
First we thought that you dream once or twice every night and most of it is dreamless because we didn't remember dreams
Then that we dream throughout REM.
Then that most dreams are in REM and some in nREM.
I think that it's reasonable to say that you dream constantly and there is no "dreamless sleep"
Or if there is, it's almost certainly not a thoughtless void like most people imagine, and the thoughts in it are very similar to dream thoughts (perhaps not connected in a dream...?)