dhil/phd-dissertation
1
0
Fork 0
mirror of https://github.com/dhil/phd-dissertation synced 2026-03-12 18:48:25 +00:00
Code Issues Releases Wiki Activity

Slight elaboration

Browse Source
This commit is contained in:
Daniel Hillerström
2020-10-21 01:36:14 +01:00
parent 16aff4f445
commit e1407b2eab
1 changed files with 7 additions and 1 deletions
Download Patch File Download Diff File Expand all files Collapse all files

8
thesis.tex
View File

@@ -416,7 +416,7 @@ is that of \emph{image}. The image of a total or partial function $f$,
written $\dec{Im}(f)$, is the set of values that it can return, i.e.
%
\[
\dec{Im}(f) \defas \{\, f(a) \mid a \in \dom(f) \}
\dec{Im}(f) \defas \{\, f(a) \mid a \in \dom(f) \}.
\]
@@ -431,6 +431,12 @@ written $\dec{Im}(f)$, is the set of values that it can return, i.e.
to be a bijective.
\end{definition}
%
An injective function guarantees that each element in its image is
uniquely determined by some element of its domain.
%
A surjective function guarantees that its domain covers the codomain,
meaning that the codomain and image coincide.
%
A partial function $f$ is injective, surjective, and bijective
whenever the function $f' : \dom(f) \to \dec{cod}(f)$, obtained by
restricting $f$ to its domain, is injective, surjective, and bijective