From “The Big Bang Theory” by Steve Holder, posted here on Helium:
“According to the Big Bang Theory, the universe used to be extremely small, unbelievably hot, and incredibly dense. Everything that existed was condensed into a compact space. It was not just a spot IN the universe, it was the ENTIRE universe. Absolutely nothing, not even empty space, existed outside of this miniaturized cosmos.
“Then, 13.7 billion years ago, something happened. Everything contained in that mini-universe began expanding outward extremely rapidly. The Big Bang Theory doesn’t explain why, but the sudden, rapid expansion is similar to what we’d expect to happen from an enormous explosion, hence the name.
WHAT IT MEANS
If the universe was once very compact, then it had a boundary. According to the theory, you couldn’t go outside this boundary because there was no “outside.” Everything that existed was inside. You could only go so far, then you had to stop because there was no farther you could go.
Back in those “good old days” some 13 billion years ago, we could get to the edge of the universe more easily than we can today. Except of course, there was no “we” back then. But in theory, the universe once had an “edge,” a boundary, a finite limit. And if it did, then it still does.
Just as counting the grains of sand on planet Earth seems an impossible task, calculating the distance to the edges of the universe also seems impossible. That doesn’t mean there are infinite grains of sand on our planet, nor does it mean there are infinite numbers of light-years between the universe’s boundary and us.
Given our limited sensory abilities and the incredible expanding size of the cosmos, the edges of the universe are beyond our current ability to discern. But they are still there, moving away from us faster than we can imagine.
One thing compounding the problem of finding the universe’s size is how fast the universe is expanding. Within a nanosecond after discovering the outer edge, it would have moved exponentially farther away before anyone could confirm the original detection.
You could imagine that once we mastered the technology to find the boundary of the cosmos, seconds later it would have moved so much farther away that it could take centuries for us to develop a new technology to find how much farther away it went.
So, no, the universe is not infinite. It just has a size beyond our ability to measure.
In engineering, we call that “practically” infinite. But in mathematics, that’s not “actually” infinite. And what is not infinite is finite.