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・ Absorbed dose
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・ Absorbing Markov chain
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・ Absorbing set (random dynamical systems)
・ Absorbing the Disarray
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Absorption (logic)
・ Absorption (pharmacokinetics)
・ Absorption (psychology)
・ Absorption (skin)
・ Absorption band
・ Absorption cross section
・ Absorption edge
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・ Absorption heat pump
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・ Absorption of water
・ Absorption refrigerator
・ Absorption spectroscopy
・ Absorption unit
・ Absorption wavemeter


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Absorption (logic) : ウィキペディア英語版
Absorption (logic)

Absorption is a valid argument form and rule of inference of propositional logic.〔http://www.philosophypages.com/lg/e11a.htm〕 The rule states that if P implies Q, then P implies P and Q. The rule makes it possible to introduce conjunctions to proofs. It is called the law of absorption because the term Q is "absorbed" by the term P in the consequent.〔Russell and Whitehead, ''Principia Mathematica''〕 The rule can be stated:
:\frac
where the rule is that wherever an instance of "P \to Q" appears on a line of a proof, "P \to (P \and Q)" can be placed on a subsequent line.
== Formal notation ==
The ''absorption'' rule may be expressed as a sequent:
: P \to Q \vdash P \to (P \and Q)
where \vdash is a metalogical symbol meaning that P \to (P \and Q) is a syntactic consequences of (P \rightarrow Q) in some logical system;
and expressed as a truth-functional tautology or theorem of propositional logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in ''Principia Mathematica'' as:
:(P \to Q) \leftrightarrow (P \to (P \and Q))
where P, and Q are propositions expressed in some formal system.

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