Apparently since US is endorsing Israel, what Israel govt is doing is fully right and any opposition can be reduced to meaningless squabbles, smh (/s)
When talking about vector space, you usually need the "scalar (field)", and scalars need inverse to be well-defined.
So for integers, the scalar should be integer itself.
Sadly, inverse of integers stops being an integer, from where all sorts of number theoretic nightmare occurs
Instead, integers form a ring, and is a module over scalar of integers.
It is just to consider polynomials and functions as vectors, and apply our meager intuition on 3d spaces. By introducing norms (size), you recover the "size and direction" analogy.
It was far long ago when I learned these stuff, but I recall that orbitals is more about probability to exist at certain points. So orbitals are more "diffuse" and "fuzzy": there is a probability of an electron to exist 5m away from its nuclei, just the probability is astronomically low. Hence, there is no concept of concrete "touch" at this level.
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