Yes the Universe is expanding into “Nothing” Just what the heck is “Nothing”?
Is it stable? Does Universe expand from nothing into nothing?
I guess won’t ask why, because nobody really knows.
So, when I croak, will the Universe expand into Me? Or what was me? 
It’s a fun mental exercise to try to arrange in order of how much nothing there is in:
The Null Set
Zero
Vacuum
Empty Space
Hole
something that has no name
something you can’t even imagine
Well, I don’t think it’s the case that the universe is expanding from nothing. I’m sure that one of the physicists will be around to explain things more thoroughly, but as far as I’m aware, the universe is creating more space “in between” the space that already exists. That is, if you have two points that right now are 1 megaparsec away, in one second, they will be 1 megaparsec and 70 kilometers away. So, the universe isn’t expanding at the edges, but all around.
Also, as far as I’m aware there is no edge to the universe. That is, there is no border between space and nothing. It works vaguely like sphere does in two dimensions. If you walk along the sphere, you will never get to an edge. The universe is kind of like that, except that it’s also “spherical” like this in the up and down direction. This can be hard to imagine.
Now, it is most likely the case that the universe is not like this exact description I’ve given (this would mean that space is not flat in a certain sense, and as far as we can tell, it’s really, really close to flat). But it’s an idea of how to have edgeless objects.
Physically what expansion means is that distance between objects is getting larger as a function of time (and distance). What the universe is expanding into is a moot point, does it have to expand in to anything?
I like to think about spacetime geometrically and I think of it expanding in the same way as a cone ‘expands’ as you move from itr’s apex to it’s base
If we really had to have it espanding in to something, we could I suppose have it expanding in to some imagianry 5th dimension (the other 4 dimensions being the dimensions of time and space), but that 5th dimension is completely redundant anyway to our description of expansion so imagining it is not really necessary.
Expansion in a technical sense really has quite a narrow meaning as generally what is being talked about is the behaviour of the spatial coordinates in FLRW coorindates as a function of the time cooridinate.
.
It doesn’t have to be expanding ‘into’ anything - in fact, it can’t be. The universe is everything - it can’t be expanding into something that isn’t part of ‘everything’.
The universe is everything there is
That everything is a quantity
If that quantity can change, then the universe can expand without encroaching on anything else.
There might be some higher-dimensional realm in which our universe is “embedded.” Sort of like how “Flatland” is embedded in three-dimensional space.
I like Zeldar’s list of “nothings.” What about “self-contradictory formulas” as an entry into the list? For my part, I equate their truth-value to the “empty set.” But the three-pronged blivet (or “poiuyt”) in my living room is making me wonder…
Trinopus
To get on my soap box for a minute, I think that your question should be the most important question in physics. Why is there something instead of nothing? Why are there physical laws at all? If there are physical laws inside the universe, why wouldn’t there be laws “outside” of the universe? After all, if there is “nothing” outside our universe, then it should be on equal footing with the “nothing” from which the universe sprang. So by symmetry, there should be no distinction from “nothing” and our universe. Our universe is the definition of what “nothing” is in practice. Conceivably, in some sense, our observable universe is the sum result of the nonexistence of rules and all possibilities being realized simultaneously.
Assuming for a moment that the concept of ‘outside our universe’ is even meaningful, by what criteria can you compare the nothing there to the nothing that pre-existed the universe? By definition, ‘nothing’ has no properties by which to make the comparison.
Which is heavier: a non-existent African elephant, or a non-existent Indian elephant? Are both non-existent elephants the same colour?
Assuming the universe is a computer program, “nothingness” to us is really the memory space reserved for operating system processes. Since Universe OS is closed-source, we can’t see anything in this region. Black holes are fatal exceptions where the source code may have been exposed but we didn’t have appropriate system privileges to view it.
Well, precisely. By definition, the two “nothings” are equal, and therefore should not be thought of as distinct. In other words, if the concept of ‘outside our universe’ were meaningful, there would be no distinction between the ‘inside’ and the ‘outside’ anyways.
Your bit about non-existent elephants misses my point (which is a very hard point to make, admittedly). The point is, try to imagine what would ‘happen’ (I know just words are not quite up to the task here, given that there would be no concept of even time) if the universe were simply the ‘state’ of there being no imposition of rules or structure of any kind, as would be true if there is no God or arbitrary axioms imposed by some authority. The universe would ‘start’ with what I would define to be ‘nothing’, and it is a ‘nothing’ that can’t be imposed to be ‘nothing’ from on-high, which seems to be how you are defining it. The apparent result of such a situation is the universe we find ourselves in.
Except lost dryer socks apparently. 
Well, yes, but no. The’re not distinct, but neither are they not-distinct, because they’re not anything - since nothing meaningful can be said about something that has no meaningful properties, including existence
Comparing nulls is like this in some fields of computing, incidentally - it’s not appropriate to say that two cases of null are either different, or the same.
That seems a different proposition to ‘nothing’, to me. That’s ‘something, but nothing in particular’.
The OP asked the question:
Yes the Universe is expanding into “Nothing” Just what the heck is “Nothing”?
In this context, I don’t agree that it is reasonable to define ‘nothing’ as a ‘null set’, because outside the universe there is no authority to ‘mandate nullness’. ‘Outside’ the universe there is merely the ‘absence of authority,’ as it were. I think that is true by definition.
As I said I don’t think it is relevant to discuss null sets here, but even if we were I can’t say I understand your argument about not being able to compare them. This may be because I’m not familiar with theoretical computer science. Regarding null sets in physics/philosophy/math, in general you can certainly compare them and discuss their properties.
I think this is the point on which we differ. ‘Outside the universe’ is the same as ‘North of the north pole’. It’s *nothing *not in the sense of being empty or unmanaged space, it’s *nothing *in the sense of not existing at all.
And for things that don’t exist, a statement that they are similar to X is equally truthful as a statement that they are dissimilar to X.
It was practical computing applications I’d encountered it, rather than theoretical, but I propose we not continue that sidetrack, unless you particularly want to.
First of all, just to be clear, I am not at all referring to ‘empty’ or ‘unmanaged space’ which assumes the existence of some form of structure. (You probably understand this; language is not equipped to convey these ideas compactly.)
And right, I don’t agree, due to the following reasoning:
Suppose, for the sake of argument, that at some point the universe did not exist. (It is expanding after all, and suppose at some point in the past it had zero size). If the universe did not exist, then the only ‘thing’ that existed was, as you put it, ‘not existing at all.’ And yet it is from this ‘thing’ that the universe arose. I would therefore argue that the notion of ‘not existing at all’ is unphysical (by demonstration).
Surely you can define ‘outside the universe’ in whatever way you want. But definitions and reality are not the same thing. I’m arguing that in reality there isn’t any meaningful distinction between ‘outside’ and inside, and if you choose to define outside the universe in such a way that it is distinct from the inside, you are doing it wrong!
The best metaphor for it, as described to me, is to think of spacetime like a balloon being inflated. The air inside and around the balloon is the “nothing” you’re referring to. It doesn’t matter what it’s made of, because it isn’t really being expanded “into.” The surface of the balloon is the only surface of spacetime, and it’s the only route through which we can travel and see things. The air around the balloon is not the balloon, will never be part of the balloon, and can never be traversed by beings stuck to the balloon’s surface.
For an example of what I mean, consider the possibility that ‘nothing existing’ is not possible. Anything and everything imaginable and not imaginable exists. But observable? Only that which is correlated with coherent self-aware narratives that anthropically pluck themselves out of the morass.
It sounds like you’re saying the ‘nothing’ from/in which the universe arose is actually a kind of something. If so, I don’t think I necessarily agree.
I’m not sure there is a good word for it, but it’s the blankest slate I can possibly imagine: that which is in the absence of all else, that which is in the absence of any arbitrarily imposed fabric of space time, laws of physics, substance… that which is ‘outside’ our universe.
My head hurts!!