Post on bitcointalk in technical discussion
I am trying to understand the bitcoin arithmetic, as opposed to the mathematics. A couple of websites mention that dividing with the elliptic curve points is impractical so they multiple by the inverse.  Just in case it matters my primary reference is this site:   
https://learnmeabitcoin.com/technical/cryptography/elliptic-curve/
Trying to stay with the basics, multiply a by the inverse of b is the same as dividing by b.  But arithmetically the inverse of a is found by dividing a into 1.  The result is between 0 and 1.  But to my limited knowledge, elliptic curves are integer arithmetic.
The declaration of the Ruby function is
def inverse( a, m = $p)
I don’t know Ruby. 
It looks like a is a single variable, and so is m, the modulus value, presumably “the” modulus used in the Bitcoin elliptic curve.  Both are integers, not points. 
So what really huge concept am I missing?