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{{DISPLAYTITLE:{{M|\mathbb{R}_+}} (notation)}}
==Notation==
: {{Highlight|Do not use this notation}}
The notation {{M|\mathbb{R}_+}} is horribly ambiguous, it could easily mean either of the following:
# {{M|1=\mathbb{R}_+:=\{x\in\mathbb{R}\ \vert\ x\ge 0\} }}
#* Which is used by{{rAPIKM}}
# {{M|1=\mathbb{R}_+:=\{x\in\mathbb{R}\ \vert\ x > 0\} }}
{{Todo|Find reference for this}}
==Solution==
Use {{M|\mathbb{R}_{\ge 0} }}, this requires one more letter and there is literally no way to interpret this wrongly. Both {{M|\mathbb{R}_{\ge 0} }} and {{M|\mathbb{R}_{> 0} }} are extremely clear. Furthermore this notation extends naturally to things like {{M|\mathbb{R}_{\ge 5} }} or {{M|\mathbb{R}_{\le 0} }}, it is obvious what these mean. See [[Denoting commonly used subsets of R]]
==Ambiguities==
* ''[[positive]]'' ({{M|+}}) means {{M|>0}} and we use ''[[non-negative]]'' to mean {{M|\ge 0}} (as this is literally ''not negative'')
==Problems==
* If we use {{M|\mathbb{R}_+}} to denote {{M|\ge 0}} how would we denote {{M|>0}}?
==Conflicts==
When we use {{M|\mathbb{N}_+}} it is pretty clear that this means the set {{M|\{1,2,\ldots,n,\ldots\} }}, that is {{M|\mathbb{N}_+:=\{n\in\mathbb{N}\ \vert\ n>0\} }} - this conflicts with definition 1) above and thus using {{M|\mathbb{R}_+}} as {{M|\mathbb{R}_{\ge 0} }} violates the [[Doctrine of least surprise]]
==References==
<references/>

[[Category:Index]]
[[Category:Notations]]
[[Category:Spaces]]
[[Category:Notations to avoid]]
[[Category:Ambiguous notations]]