[westurner]

Multiplication is repeated Addition. Exponentiation is repeated Multiplication.

  assert 2+3 == 5
  assert 2*3 == 6 == 2 + 2 + 2
  assert 2**3 == 8 == ((2+2) + (2+2))

And then fractional countability;

  assert 2.5*2 == 5 == (2*2) + (0.5*2)
  assert 2.5*10 == 25
  assert 2.5*100 == 250
  assert 2.5*104 == 260 == (2.5*100)+(2.5*4)

Functions are quickly demo'able with Desmos or Geogebra, or SymPy and matplotlib:

  # f(x) = x+1
  def f(x):
    return x+1
  assert f(0) == 1
  assert f(1) == 2
  assert f(999) == 1000

Calculus derivatives:

  # N-th derivatives of displacement; velocity, acceleration, jerk, jounce

  # (time t seconds, meters)
  xyvals = [(0,0), (1, 10), (2, 120)]

  # velocity:
  10-0 / 1-0 = 10m/s 
  100-10 / 2-1 = 110m/s