Questions regarding the popular "finite but unbounded" universe Regarding the finite but unbounded universe, according to my understanding some people come up with this idea because of the limitation of tools to detect what's "outside" the cosmic horizon (or "boundary") of the observable universe so they assumed the universe is finite but unbounded. Is not it?
I have two assumptions about what are possibly there outside the cosmic horizon of the observable universe a.k.a finite but unbounded universe, first it is absolute nothing and second there are something all the way through infinity. But if we assumed there is absolutely nothing outside the finite but unbounded universe, is it logical to assumed something can resided in nothing? 
If we define our terms precisely in order to have better comprehension, I think the universe as a whole is infinite if we defined universe as everything including what is beyond this and that ad infinitum.
The point of my question is, if there is indeed such thing as finite but unbounded universe, why is it possible for it to exist in absolute nothing?  
 A: Your confusion comes from the fact that when you think of a universe which has the Topology if a sphere/torus/what-have you (something compact — i.e. “finite but unbounded”), you’re thinking of this object being embedded in some higher-dimensional space (for instance, one usually thinks of the 2-sphere as being embedded in three-dimensions).
Imagine being a “flatlander” — a two dimensional person living in a two dimensional world. Now assume this flatlander lives on a sphere. He can go around the sphere and come back to where he started. This is in effect a consequence of the geometry of his world. When doing his mathematics to write this down, he could say that his world is embedded in a higher-dimensional space. However, he could also describe his world completely without ever referring to this “extra” dimension, by using the intrinsic geometry of his world as a starting point.
Basically, we tend to think of the universe in terms of an intrinsic (we live on the sphere) as opposed to an extrinsic (the sphere is embedded in a higher-dimension) point-of-view. The drawback of working with an extrinsic description is that there is no physical interpretation of the space around the embedded sphere, which is the root of your misunderstanding. If you work in the intrinsic description, there is no need to appeal to an extra dimension, and there is nothing “outside” the universe.

I also want to point out that the idea of a compact universe doesn’t come from physicists trying to resolve our inability to observe outside our physical universe. Rather, the compact spherical (positive-curvature) model comes from the Einstein equations applied to large-scale cosmology, if the energy density of the universe is above a certain number (which we have reason to believe it isn’t). In addition, if the energy density corresponds exactly to this “critical” density, space would be flat and unbounded on large scales, and if the mass density is less than thus critical density, the universe would have an unbounded “saddle” (hyperbolic) shape at large scales. This is an actual prediction of General Relativity, and not an ad-how explanation/model.
A: 
Regarding the finite but unbounded universe, according to my understanding some people come up with this idea because of the limitation of tools to detect what's "outside" the cosmic horizon (or "boundary") of the observable universe so they assumed the universe is finite but unbounded. Is not it?

No, you're misunderstanding. These are three different things:
Finite but unbounded universe: This is a universe whose spatial topology is that of a sphere. It wraps around.
Cosmic horizon: This is the limit on how far we can see right now because light has had a finite time to propagate.
Boundary: A manifold with boundary contains points that do not have a topological neighborhood of points surrounding them. This breaks the equivalence principle and the standard formulation of general relativity.
