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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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Examples
One axiom of modern warfare is that airpower cannot conquer, control or hold ground.
Newton's axiom on slicing the pie to satisfy musical harmonies is reminiscent of Kepler's Pythagorean speculations.
It has long been an axiom that history is re-written by each generation in terms that make sense to it.
Like all absolutist dogmas, this combination of axiom and corollaries appeals in its simplicity and directness.
I start from the simple axiom that I own myself, that my life belongs to me and not to someone else.
In set theory he made important contributions to the axiom of choice and to the continuum hypothesis.

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