# Extend the domain of maximum and minimum to include empty collection?

**URL:** <https://discourse.julialang.org/t/extend-the-domain-of-maximum-and-minimum-to-include-empty-collection/5135>\
**Category:** Internals & Design\
**Tags:** question, proposal\
**Created:** [July 30, 2017, 10:21am UTC](https://discourse.julialang.org/t/extend-the-domain-of-maximum-and-minimum-to-include-empty-collection/5135 "2017-07-30T10:21:20Z")\
**Posts on this page:** 1\
**Showing post:** 3

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**Author:** ![klacru](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/klacru/32/27890_2.png) [@klacru](https://discourse.julialang.org/u/klacru)\
**Post date:** [August 1, 2017, 9:07am UTC](https://discourse.julialang.org/t/extend-the-domain-of-maximum-and-minimum-to-include-empty-collection/5135/3 "2017-08-01T09:07:37Z")

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Thanks for your response. I agree, that for `AbstractFloat` types, the suggested return values (`-Inf` resp. `Inf`) seem more reasonable that the `typemin` resp. `typemax` outputs for other `Real` types.  
In the meanwhile, I think, the problem is even more general, I restrict to the `maximum`case for now. In the `minimum `case so analogous.

`maximum(itr)` should IMHO mimic the behavior of `reduce(max, v0, itr)`, where it tries to guess the type and value of `v0` depending on `eltype(itr)` if `itr` is empty. “`v0 must be a neutral element for op that will be returned for empty collections.`” according to the documentation of `reduce`. The neutral element of `max` is any lower bound on the type on which `max` operates. Now lower bounds are not implemented for all kinds of types, which implement `max` or `<`. So in the moment `typemin` is the best guess we have in the general case.  
We could also introduce a new function like `lowerbound` or so, which explicitly provide the value per type.  
Here a list of lower bounds for some types, not restricted to `Real`:

| Type | lower bound | upper bound |
| --- | --- | --- |
| Int32 | ? | ? |
| UInt32 | UInt32(0) | ? |
| Float16 | -Inf16 | Inf16 |
| BigInt | no representation of -∞ provided | no representation of ∞ provided |
| BigFloat | typemin(BigFloat) | typemax(BigFloat) |
| Rational{T} | -one(T)//zero(T) | one(T)//zero(T) |
| String | “” | nothing |
| Set{T} | Set(T) | set of all elements of type T |

The `?` means: `typemax` returns a value, which may be considered an implementation artefact but does not represent the bound of a mathematical idealization. `BigInt` suffers from the missing implementation of infinities in GMP.  
The `Set` example is arguable because `<(x::Set,y::Set)` implements the usual order relation for sets, but `max(x::Set,y::Set})` should not be `ifelse( y < x, x, y)` but rather `union(x,y)`.

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