To me it seem that the naturals are discrete in nature and that zero really not a natural number or even a number. Regarding infinity we can not have a view of something where we do not have a full set handwaving shouting infinity really do not help.
For me each natural must be a continuum fractions is just a way to partition a discrete natural number. When we partition a single discrete entity of the naturals one realise that infinity is just the limit expressed. The numberline is just a figment of imagination, where we imagine discrete entities lined up.
We can take a cut anywhere to represent 7 so the set is a much better analogy to magnitudes then the numberline.