Not so. The null set contains nothing. A set is not the same as its contents.
The set {x,y,z} has three elements. The set {x,y,z,null set} has four elements. They are not equal. What you have demonstrated is that the null set is a subset of every set. It is not contained in every set.
I’m not a mathematician so I can’t argue with everyone’s null sets and whatnot, but speaking from the standpoint of theoretical physics the universe, matter/energy and space/time and alternate dimensions is made up of super strings. (String Theory.) The whole universe is freestanding waves on these strings.
Everybody posting so far has talked about matter but no one has made the suggestion that space itself counts as a thing. To be outside of space itself is a condition which I really sincerely doubt the human mind can comprehend. Not just no matter, not just blackness, but nothing. That is what nothing is. It’s hard to even imagine. You can unravel a hypercube but it’s impossible to unravel nothing.
Nothing is a negative concept; it’s the absence of something (or the absence of everything - same thing, because everything is the largest possible set of somethings).
it’s nonsense to talk about the ‘presence of nothing’, think about it, if you could have the presence of nothing, you should be able to have ‘two nothings’ or ‘an abundance of nothings’
So by [this] definition everything can’t include nothing, otherwise the presence of everything would have to exclude the presence of everything.