Good.
That is a clear case of an absolute infinite length. It cannot be increased.
Three comments:
1. It is NOT the 'absolute infinity' that Cantor was talking about. In fact, the size of the line is very small in the hierarchy that Cantor discovered.
2. It most certainly *can* be increased: simply think of the line as being inside of a plane. The plane is undeniably larger than the line, right?
3. More relevant to 'expansion', imagine two of those lines, parallel to each other. Label the points on the upper line with numbers (a number line as in elementary school). Also label the lower line with numbers, but have the numbers placed twice as far apart as they are in the upper line.
Now imagine the upper line expanding to become the lower line in such a way that the numbers are aligned. If you want, think of arrows from the number on the upper line to the same number on the lower line.
The distances between all of the points increased by a factor of 2. So the upper line can expand to give the lower line. Yes, even though both are infinite in length.
Every *finite* piece of the upper line has its length double in the lower line.
Again, I have no issue with that. It cannot be increased.
See above.
Yes .. we do have evidence that the universe is expanding.
It is just that I find that it is not coherent to have an expanding volume that is infinite. It is a contradiction.
To suggest that the distance between galaxies are moving away from each other, and the volume correspondingly increases contradicts the notion of the behaviour of a non-finite quantity.
That is, "as an infinite space grows, it remains infinite" is a paradoxical concept. Something that cannot be increased, cannot grow.
See above.
Now, your suggestion that it is only the distance between galaxies that is increasing, and the volume of space is constant is in question. It is understood that it is the metric of spacetime itself that increases.
The metric is the mathematical description of the distances. When you say that the metric increases, that is the same as saying the distances increase, which is the same as saying things are expanding.