[add md6 file]

Author: 황기성

_posts/2025-12-11-set_5.md

@@ -43,4 +43,9 @@ So, it can have several x and only one
 
 The definition of serial is $\forall x\in A, \exist y\in B \: s.t. \: xRy$.
 
-This tells us that it is exist y for each x.
+This tells us that it is exist y for each x.
+
+### etc
+When there is an element (a, b) of relation R, (a, b) is called a pair, a is called the first component, and b is called the second component.
+
+

_posts/2026-01-26-set_6.md

@@ -0,0 +1,33 @@
+---
+layout: single
+title: "5.Function"
+categories: Math
+tag: [Linear_Algebra, Set_theory]
+toc: true
+author_profile: false
+sidebar:
+  nav: "docs"
+use_math: false
+---
+
+
+### Function
+A function is a relation $f \sub A \times B$ that is functional and serial. <br>
+This means that each element of the domain is related to exactly one element of the codomain, and every element of the domain appears in the relation. <br>
+$\forall a \in A, \exist! b \in B : f: A \rightarrow B$ <br>
+Notation: $f: A \rightarrow B$ <br>
+
+### Range
+A range is $f(A) := \{f(a) \in B| a \in A\}$.<br>
+The range of $f$ is the set of all elements in the codomain that are related to element of the domain.
+
+### 1 - 1 Function
+A one-to-one function is a function in which each element of the codomain is related to exactly one element of the domain.<br>
+$\forall b\in f(A), \exist! a\in A : f: A \rightarrow B$
+
+### 1 - 1 Correspondence
+A bijective function is a function in which each element of the codomain is related to exactly one element of the domain.<br>
+$\forall b\in B, \exist! a\in A : f A \rightarrow B$
+
+### Inverse Function
+The inverse function reverses the mapping of the original function $f:A \rightarrow B$, so that $f^{-1}: B\rightarrow A$