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  1. Wikipedia
    https://en.wikipedia.org/wiki/Axiom

    Axiom - Wikipedia

    • 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 philos… 展开

    Etymology

    The word axiom comes from the Greek word ἀξίωμα (axíōma), a verbal noun from the verb ἀξιόειν (axioein), meaning "to d… 展开

    Historical development

    The logico-deductive method whereby conclusions (new knowledge) follow from premises (old knowledge) through the application of sound arguments (syllogisms, rules of inference) was developed by the ancient Greeks, … 展开

    Mathematical logic

    In the field of mathematical logic, a clear distinction is made between two notions of axioms: logical and non-logical (somewhat similar to the ancient distinction between "axioms" and "postulates" respectively).
    These are certain … 展开

    See also

    • Mathematics portal
    • Philosophy portal
    • Axiomatic system
    • Dogma
    • First principle, axiom in science and philosophy… 展开

    Axiom, Corollary, Lemma, Postulate, Conjectures and Theorems
    An axiom would refer to a self-evident assumption common to many areas of inquiry, while a postulate referred to a hypothesis specific to a certain line of inquiry, that was accepted without proo…
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  1. Axioms and postulates are thus the basic assumptions underlying a given body of deductive knowledge. They are accepted without demonstration.
    了解详细信息：
    Axioms and postulates are thus the basic assumptions underlying a given body of deductive knowledge. They are accepted without demonstration.

    Axiom - Wikipedia

    en.wikipedia.org/wiki/Axiom
    Axioms and postulates are essentially the same thing: mathematical truths that are accepted without proof.

    Geometry: Axioms and Postulates - Spark…

    www.sparknotes.com/math/geometry3/axiomsandp…
    Theorems are proven on the basis of already proven statements (other theorems) or axioms while axioms (or postulates) are statements that are accepted as true without a proof.

    Difference between postulates, axioms, a…

    math.stackexchange.com/questions/727326/differe…
    Axioms and postulates are assumptions or statements that provide the basis for logical arguments or deductions.

    Axioms and Postulates in Geometry - Int…

    www.intmath.com/functions-and-graphs/axioms-an…
  2. 其他用户还问了以下问题
    What is the difference between axioms and postulates?
    Both axioms and postulates are assumed to be true without any proof or demonstration. They are basic truths that are obvious or declared to be true and accepted, but have no proof for that. Axioms and postulates serve as a basis for deducing other truths.

    Difference between axioms, theorems, postulates, corollaries, and

    math.stackexchange.com
    What are postulates specific to?
    Postulates are assumptions which are specific to geometry. Modern mathematics distinguishes between logical axioms and non-logical axioms, with the latter sometimes being referred to as postulates. Axioms are assumptions are used throughout mathematics and not specific to geometry.

    Axiom, Corollary, Lemma, Postulate, Conjectures and Theorems

    mathematicalmysteries.org
    Why do you prefer a postulate over an axiom?
    I personally prefer "postulate" over "axiom", since a "postulate" transparently conveys (or connotes - as in connotation) that what we are calling a postulate is "postulated" as a "supposition", from which we agree to work in building theorems or a theory.

    What is the difference between an axiom and a postulate?

    math.stackexchange.com
    What is an axiom in mathematics?
    There is a strange creature in mathematics, not typically mentioned in lower division texts, called an axiom (or, in some texts, a postulate). An axiom is a self-evident or universally recognized truth. It is accepted as true, without proof, as the basis for argument.

    0.2: Axioms, Theorems, and Proofs - Mathematics LibreTexts

    math.libretexts.org
    Are axioms considered 'obviously true'?
    In modern mathematics, axioms are not assumed to be 'obviously true'. They are merely 'background' assumptions we make. In Geometry, the terms 'axiom' and 'postulate' are essentially interchangeable. In antiquity, they referred to propositions that were considered 'obviously true'.

    Difference between axioms, theorems, postulates, corollaries, and

    math.stackexchange.com
    What are Euclid's axioms and postulates?
    In Euclid's Geometry, the main axioms and postulates are: Given any two distinct points, there is a line that contains them. Any line segment can be extended to an infinite line. Given a point and a radius, there is a circle with center in that point and that radius. All right angles are equal to one another.

    Difference between axioms, theorems, postulates, corollaries, and

    math.stackexchange.com
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  3. BYJU'S
    https://byjus.com/maths/euclidean-geometry

    Euclidean Geometry (Definition, Facts, Axioms and Postulates)

  4. Mathematics Stack Exchange
    https://math.stackexchange.com/questions/7717

    Difference between axioms, theorems, postulates, corollaries, and ...

  5. Cuemath
    https://www.cuemath.com/geometry/axioms-and-postulates

    Axioms And Postulates | Solved Examples | Geometry - Cuemath

  6. BYJU'S
    https://byjus.com/question-answer/what-is-the...

    What is the difference between an axiom and postulates - BYJU'S

  8. Britannica
    https://www.britannica.com/science/Eu…

    Euclidean geometry | Definition, Axioms, & Postulates

    5 天之前 · Euclidean geometry is the study of plane and solid figures on the basis of axioms and theorems employed by the ancient Greek mathematician Euclid. The term refers to the plane and solid geometry commonly taught in …

  9. Mathematics LibreTexts
    https://math.libretexts.org/Courses/Cosumnes_River...

    0.2: Axioms, Theorems, and Proofs - Mathematics LibreTexts

  10. Mathematics Stack Exchange
    https://math.stackexchange.com/questions/258346/...

    What is the difference between an axiom and a postulate?

  11. EMBIBE
    https://www.embibe.com/exams/euclids-definitions...

    Euclid's Geometry: Definitions, Axioms, Postulates, Examples

  12. Mathematical Mysteries
    https://mathematicalmysteries.org/axiom-c…

    Axiom, Corollary, Lemma, Postulate, Conjectures and …

    An axiom would refer to a self-evident assumption common to many areas of inquiry, while a postulate referred to a hypothesis specific to a certain line of inquiry, that was accepted without proof. As an example, in Euclid’s Elements, …