Most people believe three-dimensional space is not physical and therefore cannot have physical boundaries. If space is formless and unbounded, we can reasonably assume that space is infinite.
Officially, the analysis of space cannot proceed without a definition for infinity that all mathematicians can agree with, but this is just a technicality. A precise mathematical definition for infinity has always been out of reach.
Most everyone agrees with the logic of infinity as something without beginning or end. We can proceed with the analysis based on the logic of the definition, which allows us to describe space as having no beginning or end.
We can also proceed with a comparative analysis if we can find something to compare space to. It just so happens that a circle with perfect geometric symmetry is equal to infinity, because there are no reference points for beginning or end to be found in the circumference. A perfect circle is only theoretical, but the circle is perfectly round and all points in the circumference of the circle are seamlessly connected, and all of the points are alike.
We know perfect geometric symmetry does not exist in the universe but we do not know why. We have always assumed that perfection was beyond the realm of human experience. All we know is that there is no such thing as a perfect circle or a straight line in reality, and that time does not allow for perfection in the formation of physical geometries. Now we know that space exists as a model of perfect symmetry without the confines of geometry, and time, the universe, does not.
We never thought to look at space as perfection. Now we know perfection is all around us, provided of course, that three-dimensional space is infinite. And we know one of nature’s secrets. Nature is capable of perfection.
That still leaves us with the question of what is the nature of space. Either space always pre-existed, or space had to be engineered, like time, into existence. When mathematicians were in a search for the very first thing in existence, they reasoned that the Big Bang needed room for expression. A value of one was then assigned to three-dimensional space. The assignment is valid whether space pre-existed or did not, because it is meant to show the sequential order of nature, and to show that the universe is space dependent.
Mathematicians are still asking the question of where the number one came from. The same question is being asked in modern cosmology when we ask, what is the nature of space?