View source for K (field)

{{DISPLAYTITLE:{{M|\mathbb{K} }} (field)}}{{Stub page|grade=D|msg=Created to define what {{M|\mathbb{K} }} means when encountered as a [[field]] (eg if {{M|(X,\mathbb{K})}} is a [[vector space]] - [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 03:54, 8 April 2017 (UTC)
* Also make sure that the doctrine page lists references that this page does, as they're the same thing!}}
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==Meaning==
As per the [[Doctrine:K (field)]] we use {{M|\mathbb{K} }} to denote a [[field]] which is either the [[field of real numbers]], {{M|\mathbb{R} }}, or the [[field of complex numbers]], {{M|\mathbb{C} }}. 

This only applies if we do not explicitly define what {{M|\mathbb{K} }} is<ref group="Example">Take:
: "''Let {{M|\mathbb{K}\in\mathbb{N} }} be given and suppose {{M|X}} is a set, define {{M|z:\eq (X,\mathbb{K})}}''"
Here {{M|\mathbb{K} }} is a natural number and {{M|(X,\mathbb{K})}} is simply an [[ordered pair]].</ref>, in the absence of any mention of what {{M|\mathbb{K} }} is the doctrine applies and it is a stand in for either {{M|\mathbb{R} }} or {{M|\mathbb{C} }}.

This convention is not unusual{{rFAVIDMH}}.
===Caveats===
# If we say "let {{M|(X,\mathbb{K})}} and {{M|(Y,\mathbb{K})}} be [[vector spaces]]" it is unclear whether {{M|X}} and {{M|Y}} are both over the same field or not.
#* We will qualify this with "over the same field" or "over potentially distinct fields"; or use {{M|\mathbb{K}_1}} and {{M|\mathbb{K}_2}} if the fields will play a part in what is to come.
# If we say "let {{M|(X,\mathbb{K})}} be a [[vector space]] over the [[field]] {{M|\mathbb{K} }}" it suggests that {{M|\mathbb{K} }} is just being used to represent the field, the doctrine doesn't apply then. It'd be as if the more conventional {{M|\mathbb{F} }} were used instead.

==Examples==
<references group="Example"/>
==References==
<references/>
[[Category:Standard notation]]