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\begin{definition}[]{Sufficiency}
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A condition $P$ is called \textit{sufficient} for $Q$ if knowing $P$ is true is enough evidence to conclude that $Q$ is true.
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This is equivalent to saying $Q \Rightarrow P$.
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This is equivalent to saying $P \Rightarrow Q$.
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\end{definition}
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\begin{definition}[]{Necessity}
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A condition $P$ is called \textit{necessary} for $Q$ if $Q$ cannot occur unless $P$ is true, but doesn't imply that $Q$ is true, only that it is false if $P$ is false.
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This is equivalent to saying $P \Rightarrow Q$
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This is equivalent to saying $Q \Rightarrow P$
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\end{definition}
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\subsection{Asymptotic Growth}
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