Guess what a function converges to

converge.py

import itertools

def adjacent_pairs(g):
    a, b = itertools.tee(g)
    next(b)
    return zip(a, b)

def converge(f, vals, e=1e-9):
    for a, b in adjacent_pairs(vals):
        if abs(f(a) - f(b)) < e:
            return f(b)

# Example: show limit definition for e works for n -> -infinity too
def e_approx(x):
    return lambda n: (1 + x/n) ** n
# Start at -2 to avoid division by zero
print(converge(e_approx(1), itertools.count(-2, -1)))