Let us see if your claim is Strew Man or not.
n=1 to ∞
k=0 to n-1
X = "Dimensional space"
Y = "Dimensional element"
k_X - k_Y = 0 amount of coordinates that are used to determine k_Y location w.r.t k_X.
We get 0 amount of coordinates even if k > 0, so there are no coordinates even if the dimensional space and the dimensional element > 0.
In other words, your indication of 0 amount of coordinates does not necessarily imply 0-dimension (or as you call it: "No-dimension").
All we need is that the magnitudes of the dimensional space and the dimensional element will be the same, no matter if k = or > 0.