Yeah so there obviously are numberlines in different bases.
Let’s check base 10 first:
0-10-100-1000-10000 etc.
1-9, 10-90, 100-900, 1000-9000 etc.
So we can conjecture (obviously it’s true, but hey) that between the ‘first’ and the ‘next’ power of N (10 here) there are N-1 spots that have integers (9 here)
Well let’s check if that’s correct with base 2:
0-10-100-1000-10000
0-1-10-11-100-101-110-111-1000-1001-1010-1011-1100-1101-1110-1111-10000,
So the amount of numbers inbetween an addition of a zero is (N^amount of zeros)-1 counted from the beginning of the zeros (disregarding the very first 0). So you can use the same numberline, but for N=2, N=3, etc have less numbers between the ‘powers’ (when a 0 gets added) while just using the same numberline, and obviously for bases higher than 10 the same thing applies.
That’s if you want to do it like that. As written before, there are other ways.
But this is actually in some odd way the most natural imho.
Easy stuff I guess.
But hey, maybe someone might find it useful.
Attribution for the graph: By Original: Unknown Vector: Autopilot – Own work based on: Loglog x x2 x3.png by Luqui, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=10733674
