From Matt Springer:
Built on Facts : Physics from All Around: Via Swans on Tea, we have Assume a Spherical Physicist from the excellent blog The First Excited State. There's an exploration of several approximations, including how N + 1 = N is for all purposes true in percentage terms for very large N. But how about this one, mentioned in my undergrad thermodynamics textbook (Schroeder, if you're curious)?
(10^23)N = N
You don't believe me, but it's in some respects true for very large N.... Yeah, the approximation is inaccurate by a factor of Avogadro's number. But in lots of thermodynamics calculations that's a trivial error...