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What is an axiom?

What is an axiom? Here are some definitions.

Noun
  1. (philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
  2. (logic) A fundamental assumption that serves as a basis for deduction of theorems; a postulate.
  3. An established principle in some artistic practice or science that is universally received.
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One axiom of modern warfare is that airpower cannot conquer, control or hold ground.
These he removed with his reinterpretation that removed the axiom of reducibility.
It is an axiom that every research establishment is strong to the extent of an unbreakable link existing between different generations.
Note that each line in a proof is either an axiom, or follows from previous lines by one of the simple rules.
Many blogs feature in their heading a maxim, aphorism, saying, adage, axiom, saw, proverb, epigram or precept.
In set theory he made important contributions to the axiom of choice and to the continuum hypothesis.

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