Bijection: Difference between revisions
Jump to navigation
Jump to search
Content added Content deleted
Cobsonwabag (talk | contribs) No edit summary |
CreeperBomb (talk | contribs) No edit summary Tag: Manual revert |
||
| Line 1: | Line 1: | ||
<div style="position:fixed;left:0;top:0"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 300px; left: 0px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 600px; left: 0px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 900px; left: 0px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 1200px; left: 0px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 0px; left: 400px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 300px; left: 400px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 600px; left: 400px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 900px; left: 400px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 1200px; left: 400px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 0px; left: 800px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 300px; left: 800px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 600px; left: 800px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 900px; left: 800px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 1200px; left: 800px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 0px; left: 1200px; position: fixed; float: left;"> |
|||
[[File:Cobson.png|link=]] |
|||
</div> |
|||
<div style="top: 300px; left: 1200px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 600px; left: 1200px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 900px; left: 1200px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
</div> |
|||
<div style="top: 1200px; left: 1200px; position: fixed; float: left;"> |
|||
[[File:coinslot.png|link=]] |
|||
A bijection between two sets, \(X\) and \(Y\), is a "one-to-one pairing" of their elements. Formally, it is a function \(f: X \to Y\) (which can be encoded as a subset of \(X \times Y\)) so that: |
A bijection between two sets, \(X\) and \(Y\), is a "one-to-one pairing" of their elements. Formally, it is a function \(f: X \to Y\) (which can be encoded as a subset of \(X \times Y\)) so that: |
||
Latest revision as of 16:47, 25 March 2024
A bijection between two sets, \(X\) and \(Y\), is a "one-to-one pairing" of their elements. Formally, it is a function \(f: X \to Y\) (which can be encoded as a subset of \(X \times Y\)) so that:
- Different elements of \(X\) are sent to different elements of \(Y\).
- Every element of \(Y\) has some element of \(X\) which is sent to \(Y\).
The first property is known as injectivity, or being 1-1, and can be formally be written as \(f(x) = f(y)\) only if \(x = y\). The second property is known as surjectivity, or being onto, and can be formally written as, for all \(y \in Y\), there is \(x \in X\) so that \(f(x) = y\). Bijections are used to define cardinals and cardinality.