Homography: Difference between revisions

Revision as of 09:41, 3 February 2014

In mathematics, the characteristic sequence of a given sequence s is a sequence of 1s and 0s which tells which elements of s are in some set.

Given two sets $A \subseteq B$ and a sequence s = $⟨ s_{n} : n \in ℕ ⟩$ of elements of $B$ , the characteristic sequence of $s$ is the sequence $⟨ c_{n} : n \in ℕ ⟩$ defined so that $c_{n} = 1$ if and only if $s_{n} \in A$ :

c_{n} = {\begin{cases} 0 & s_{n} \in̸ A, \\ 1 & s_{n} \in A . \end{cases}

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+{{Orphan|date=October 2012}}
+In [[mathematics]], the '''characteristic sequence''' of a given [[sequence]] ''s'' is a sequence of 1s and 0s which tells which elements of ''s'' are in some [[Set (mathematics)|set]].
+Given two sets <math>A \subseteq B</math> and a sequence s = <math>\langle s_n : n \in \mathbb{N}\rangle</math> of elements of <math>B</math>, the characteristic sequence of <math>s</math> is the sequence <math>\langle c_n : n \in \mathbb{N}\rangle</math> defined so that
+<math>c_n = 1</math> if and only if <math>s_n \in A</math>:
+:<math>
+c_n =
+\begin{cases}
+&  s_n \not \in A, \\
+&  s_n \in A.
+\end{cases}
+</math>
+[[Category:Mathematical logic]]
+[[Category:Binary sequences]]
+{{mathlogic-stub}}