>>> 0.1 + 0.2
0.30000000000000004
which of course is an annoying encounter for the unitiated in floats, but there’s a much bigger problem, that usually isn’t noticed at all until much later, that float addition itself isn’t even associative:
>>> (0.1 + 0.2) + 0.3
0.6000000000000001
>>> 0.1 + (0.2 + 0.3)
0.6
>>> 0.1 + (0.2 + 0.3) == (0.1 + 0.2) + 0.3
False
>>>
and this is a problem, because associativity is a big underlying assumption that we commonly have for numbers, when, for example, summing a list in reverse. other common pitfalls include:
- not all numbers have an additive inverse, ie. for some number
n,n + (-n) != n. - not all numbers different than 0 have a multiplicative inverse, ie. for some number
n,n / n != 1. - addition is not commutative, ie. for numbers
ab,a + b != b + a.
and the list goes you on, you get the idea. this usually isn’t thought of the main problems in