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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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Like all absolutist dogmas, this combination of axiom and corollaries appeals in its simplicity and directness.
Many blogs feature in their heading a maxim, aphorism, saying, adage, axiom, saw, proverb, epigram or precept.
I decline to accept as an axiom that our fate is involved in that of France.
In set theory he made important contributions to the axiom of choice and to the continuum hypothesis.
I start from the simple axiom that I own myself, that my life belongs to me and not to someone else.
It is an axiom that every research establishment is strong to the extent of an unbreakable link existing between different generations.

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