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[email protected]:1715192908
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-+++
-title = "correctness is all you need"
-author = ["santi"]
-lastmod = 2024-05-09T23:35:32-03:00
-tags = ["coq", "rust"]
-draft = false
-+++
-
-```python
->>> 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:
-
-```python
->>> (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 `a` `b`, `a + b != b + a`.
-
-and the list goes you on, you get the idea. this usually isn't thought of the main problems in