axioms

Meanings

• noun

  A set of fundamental principles or propositions that serve as the basis for a branch of mathematics or a logical system.

  - "In Euclidean geometry, the five axioms, or postulates, form the foundational principles."
  - "The axioms of set theory provide the basis for all mathematical proofs in the theory."

• noun

  A self-evident truth or principle that requires no proof.

  - "The axiom of identity states that any object is identical to itself."
  - "In logic, the law of excluded middle is an axiom that every proposition is either true or false."

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Synonyms

postulate , axioma

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Variants

List of all variants of axioms that leads to same result
axiom , axioms , axiom of choice , axioms of choice

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Etymology

origin and the way in which meanings have changed throughout history.

From the Greek word 'axioma', meaning 'that which is thought worthy or deserving'.

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Trivia

Any details, considerations, events or pieces of information regarding the word

1. The number of axioms in Euclidean geometry is five.

2. The law of excluded middle is a controversial axiom in logic, as some argue it is not self-evident.

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Related Concepts

informations on related concepts or terms closely associated with the word. Discuss semantic fields or domains that the word belongs to

1. Postulates: Axioms are often referred to as postulates in mathematics and logic. Postulates are statements that are assumed to be true without proof.

2. Principles: Axioms are also called fundamental principles, as they form the foundation for a logical or mathematical system.

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Culture

Any cultural, historical, or symbolic significance of the word. Explore how the word has been used in literature, art, music, or other forms of expression.

Axioms have played a significant role in various aspects of human civilization, from mathematics and logic to philosophy and religion.

How to Memorize "axioms"

1. visualize
   

   - To visualize the axiom of identity, imagine any object and then consider that object to be identical to itself.

2. associate
   

   - Associate the axiom of identity with the idea of self-similarity or reflexivity.

3. mnemonics
   

   - Use the mnemonic 'A is A' to remember the axiom of identity.

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