# Approximate equality

**URL:** https://discourse.julialang.org/t/approximate-equality/8952
**Category:** General Usage
**Tags:** question, bug
**Created:** [February 9, 2018, 3:10pm UTC](https://discourse.julialang.org/t/approximate-equality/8952 "2018-02-09T15:10:51Z")
**Posts on this page:** 1
**Showing post:** 41

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### Author: ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [February 11, 2018, 1:56am UTC](https://discourse.julialang.org/t/approximate-equality/8952/41 "2018-02-11T01:56:29Z")

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> [@jlperla](#):
>
> So in that case I think the warning should also be to call it with a ≈ b for vectors if the infinity norm is good enough

Actually, it defaults to the Euclidean norm (`vecnorm`) for arrays, and you can pass a different norm if desired via the `norm` keyword. It only falls back to elementwise `isapprox` if the norm is `Inf` or `NaN`. This is all documented. You don’t have to guess at the behavior.

We shouldn’t warn people against using this for arrays — if anything, we should warn people against implementing their own approximate equality for arrays, because experience suggests they will probably get it wrong. (e.g. NumPy got it wrong: their `isclose` function is only elementwise, has a nonzero default `atol`, and even has the property that `isclose(x,y)` is inequivalent to `isclose(y,x)`!)

I don’t think it should throw a `DomainError` for `x ≈ 0`. This is perfectly well defined, it just means `x == 0` since the definition is `norm(x-y) ≤ rtol*max(norm(x),norm(y))` for `atol==0`. It would be very weird for `0 ≈ 0` to throw an error rather than returning the correct answer (`true`), and this would be an especially unfortunate behavior for elementwise `isapprox` comparisons.

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