Is the space unending, i.e it has no boundaries? If yes, how can a thing exist which is non-ending? Its impossible for me to imagine something like that. Secondly, if its not and has boundaries then it must be inside some other thing which is either non-ending or itself contained in another thing. Yet, again same problem. If it is also inside some other thing, and the other thing is also inside other thing, then this series will never end. Imagining about this scenario makes me insane.
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If, by unending, you genuinely mean "no boundaries", then you can in fact easily imagine a thing with no boundaries; imagine a sphere and, well, you've done it.
Now, if, by unending, you mean "without end", then you're correct, it's difficult and perhaps impossible to imagine a thing that is unending.
But, is it impossible to imagine that space is without end? No, not if you recognize that space isn't a thing.
Now, we stray from physics to metaphysics.
If Space is a thing, an entity, then it follows that it must have identity and, to have identity, it must be finite.
But, if entities are in space, then to say that space is unending is simply to say that two entities may be arbitrarily far apart. But, and this is crucial, regardless of how large their separation, it is always, always finite.
It is the case that entities can be out of causal contact but that is in the realm of epistemology (what we can know), not metaphysics (what is).
Alfred Centauri
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The most commonly accepted model of the universe is that it is finite yet unbounded
- 1d analogy: you can walk forever around the circumference of a circle
- 2d analogy: you can fly forever around the equator of the earth
In any of these cases, you will never reach any kind of barrier or edge.
In each case the space is curved in a higher dimension.
RedGrittyBrick
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Cosmology can model space as infinite. But we are not sure how to model the very early universe as quantum gravity is needed once the density gets high enough. So there is some limit to what we can observationally infer about the size as we can't model effects beyond what light speed information could have travelled from the quantum gravity epoch.
Virgo
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It is not unending--- there is a big black wall 13.7 billion light years away (in what I consider the right definition of distance to the wall), which marks the end of what you should call space. This big black wall is the cosmological horizon, and it's like a black hole horizon, except surrounding us. We can't see past this wall, so it is consistent to say space stops there. In fact, it is probably necessary to say space stops there in quantum gravity, except we don't know how to do quantum gravity for this kind of horizon yet.
If you go there, the boundary just moves away from you to surround you in another way, so it is not paradoxical. By the time you reach the wall, the wall moves away, or if you wait long enough so that the horizon stops moving (due to the cosmological constant), when you go there, you can't come back to Earth anymore. So the limitless thing is gone, space is finite. It isn't necessary to say it is contained in something bigger, because we know what the natural boundary to a finite space can be--- one possibility is that it's a horizon. Another possibility is just a space that closes in on itself, like a sphere (but this was another answer).
This argument you give appears almost verbatim in the beginning of Aristotle's physics, and it, like everything else Aristotle writes, is both trite and wrong.
