On the other hand, floating types have density much smaller than 1, which means that there are real numbers unrepresented between consecutive floating values (i.e. there are gaps).
In the real numbers are chosen in such a way that the probability that the number lies in any particular subinterval of this unit interval is equal to the length of the subinterval.
If we were dealing with higher orders of infinity, such as that of the real numbers, these structured strategies would no longer be possible as we have no way to systematically include every number.
But just to make this in real numbers, if I had 7 factorial over 7 minus 2 factorial, that's equal to 7 times 6 times 5 times 4 times 3 times 3 times 1.
But if vectors are not fundamentally lists of real numbers, and if their underlying essence is something more spatial, that just begs the question of what mathematicians mean when they use a word like space or spatial.