SkipCaptcha, Automoderated users, edit
3,266
edits
Changes
Jump to navigation
Jump to search
mLine 1:
Line 1: − +
And the result is a theorem.
A '''postulate''' is a statement that is assumed to be true without proof. [[Euclid]], the father of geometry, based ''The Elements'' on ten such statements, divided into five "[[axiom]]s" and five "postulates."<ref>Euclid. ''The Elements''.</ref> These are used as foundation for geometry<ref>"1.1: Definitions, Theorems, and Postulates." ''Beauty, Rigor, Surprise''.</ref> and occasionally applied to other sciences, such as [[special relativity]].<ref>http://casa.colorado.edu/~ajsh/sr/postulate.html</ref><ref>https://www.nobelprize.org/educational/physics/relativity/postulates-1.html</ref>
A '''postulate''' is a statement that is assumed to be true without proof. [[Euclid]], the father of geometry, based ''The Elements'' on ten such statements, divided into five "[[axiom]]s" and five "postulates."<ref>Euclid. ''The Elements''.</ref> These are used as foundation for geometry<ref>"1.1: Definitions, Theorems, and Postulates." ''Beauty, Rigor, Surprise''.</ref> and occasionally applied to other sciences, such as [[special relativity]].<ref>http://casa.colorado.edu/~ajsh/sr/postulate.html</ref><ref>https://www.nobelprize.org/educational/physics/relativity/postulates-1.html</ref>
In ordinary discourse about a subject in mathematics or science, the terms "axiom" and "postulate" are often not distinguished—they are the statements that one takes as true from the outset, that one does not need to prove. One then uses those to prove other statements. The difference is that postulates are initial statements relating to the subject matter, such as the geometrical postulates (including Euclid's fifth postulate, below) about angles and lines. Axioms, on the other hand, tend to be more universal statements about logic, such as "if X=Y, then Y=X".
In ordinary discourse about a subject in mathematics or science, the terms "axiom" and "postulate" are often not distinguished—they are the statements that one takes as true from the outset, that one does not need to prove. One then uses those to prove other statements, which are then called [[theorem]]s. The difference is that postulates are initial statements relating to the subject matter, such as the geometrical postulates (including Euclid's fifth postulate, below) about angles and lines. Axioms, on the other hand, tend to be more universal statements about logic, such as "if X=Y, then Y=X".
==Euclid's fifth postulate==
==Euclid's fifth postulate==