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Guilherme Mazui

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What is the Difference Between Axioms and Postulates?

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The main difference between axioms and postulates lies in their scope and applicability within different fields of science. Both axioms and postulates are assumptions that are considered to be self-evident and universally true, but they are not specifically proven. Here are the key differences between the two:

  • Axioms: These are self-evident assumptions that are common to all branches of science. They are not specifically linked to geometry or any other particular field. A well-known example of an axiom is the statement "halves of equal are equal".
  • Postulates: These are specific to a particular field, such as geometry. Postulates are assumptions that are considered to be true within that field, but they are not applicable to other fields of science. Euclid, the Greek mathematician, used the term "postulate" for assumptions that were specific to geometry.

In summary:

  • Axioms are self-evident truths that are applicable to all fields of science, while postulates are specific to a particular field, such as geometry.
On this page
  • What is the Difference Between Axioms and Postulates?
  • Comparative Table: Axioms vs Postulates

    • Comparative Table: Axioms vs Postulates

    Here is a table comparing the differences between axioms and postulates:

    Feature Axioms Postulates
    Definition Axioms are self-evident assumptions that are common to all branches of science. Postulates are specific to a particular field and are used as a basis for deducing other truths within that field.
    Application Axioms are applicable to any field in science. Postulates apply to specific fields, such as geometry.
    Provisability Axioms are not provable from other axioms. Postulates can be provable to axioms.
    Examples "Things which are equal to the same thing, are equal to one another". Euclid's postulate: "It is possible to produce a finite straight continuously in a straight line".

    Both axioms and postulates are assumed to be true without any proof or demonstration. They serve as a basis for deducing other truths in their respective fields.

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    Guilherme Mazui

    Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.