Use python to calculate a special limit?

Question

I want to calculate this expression: (1 + 1 / math.inf) ** math.inf, which should evaluates to e. However Python returns 1. Why is that? =====UPDATE======== What I want to do here is to derive the effective annual rate from user's input, APR (annual percentage rate). def get_EAR(APR, conversion_times_per_year = 1): return (1 + APR / conversion_times) ** conversion_times - 1 I would want this expression to also apply to continuous compounding. Yes I understand I can write if statements to differentiate continuous compounding from normal cases (and then I can use the constant `e` directly), but I would better prefer an integrated way.

Answer 1

You cannot do usual arithmetic with infinity (even in pure mathematics.) For example, you will find that 1/math.inf evaluates to 0 in python. This is symbolic and by mathematical convention. So, in fact the symbol 1/math.inf is being stored as 0, so your "limit" is being evaluated as 1**math.inf, and defaulting by the algebra rule that 1**anything=1.

You can instead opt for using sympy, which after installation can be used to evaluate limits.

import sympy as sym

x = sym.Symbol('x')

sym.limit((1+1/x)**x, x, sym.oo)

If you need only store the value "e" for future computation, you can always store it as a variable for sufficiently large numbers, that is e=(1+1/10000)**10000.

If you want a truly robust algebra/calculus package I recommend using SageMath, which is built on top of python and completely open source.