SP20:Lecture 8 prep

From CS2800 wiki

This lecture we will discuss cardinality.

Please come to lecture with the following definitions (it helps to draw yourself a picture of a surjection or an injection to see which corresponds to [math]\href{/cs2800/wiki/index.php/%5Cleq}{\leq} [/math] or [math]\href{/cs2800/wiki/index.php/%5Cgeq}{\geq} [/math]):

Definition:
If [math]A [/math] and [math]B [/math] are sets, then [math]|A| \href{/cs2800/wiki/index.php/%E2%89%A4}{≤} |B| [/math] means that there exists an injection [math]f : A \href{/cs2800/wiki/index.php/%E2%86%92}{→} B [/math]
Definition:
If [math]A [/math] and [math]B [/math] are sets, then [math]|A| \href{/cs2800/wiki/index.php/%E2%89%A5}{≥} |B| [/math] means that there exists a surjection [math]f : A \href{/cs2800/wiki/index.php/%E2%86%92}{→} B [/math]
If [math]A [/math] and [math]B [/math] are sets, then [math]|A| \href{/cs2800/wiki/index.php/Equality_(cardinality)}{=} |B| [/math] means that there exists a bijection [math]f : A \href{/cs2800/wiki/index.php/%E2%86%92}{→} B [/math]