What does axioms mean?

Definitions for axioms
ax·ioms

This dictionary definitions page includes all the possible meanings, example usage and translations of the word axioms.


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Wiktionary

  1. axiomsnoun

    Plural form of axiom.

Wikipedia

  1. axioms

    An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (axíōma), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning.In mathematics, an axiom may be a "logical axiom" or a "non-logical axioms". Logical axioms are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (A and B) implies A), while non-logical axioms (e.g., a + b = b + a) are substantive assertions about the elements of the domain of a specific mathematical theory, such as arithmetic. Non-logical axioms may also be called "postulates" or "assumptions". In most cases, a non-logical axiom is simply a formal logical expression used in deduction to build a mathematical theory, and might or might not be self-evident in nature (e.g., the parallel postulate in Euclidean geometry). To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms), and there are typically many ways to axiomatize a given mathematical domain. Any axiom is a statement that serves as a starting point from which other statements are logically derived. Whether it is meaningful (and, if so, what it means) for an axiom to be "true" is a subject of debate in the philosophy of mathematics.

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Numerology

  1. Chaldean Numerology

    The numerical value of axioms in Chaldean Numerology is: 3

  2. Pythagorean Numerology

    The numerical value of axioms in Pythagorean Numerology is: 9

Examples of axioms in a Sentence

  1. Albert Einstein:

    Ethical axioms are found and tested not very differently from the axioms of science. Truth is what stands the test of experience.

  2. Albert Einstein:

    The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms.

  3. C. M. Cox:

    Blaise Pascal used to mark with charcoal the walls of his playroom, seeking a means of making a circle perfectly round and a triangle whose sides and angle were all equal. He discovered these things for himself and then began to seek the relationship which existed between them. He did not know any mathematical terms and so he made up his own. Using these names he made axioms and finally developed perfect demonstrations, until he had come to the thirty-second proposition of Euclid.

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Translations for axioms

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"axioms." Definitions.net. STANDS4 LLC, 2024. Web. 28 Mar. 2024. <https://www.definitions.net/definition/axioms>.

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