What is the difference between axiom and postulate? plz be detailed
Axioms and postulates are the basic assumptions and are accepted without demonstration. All other theorems must be proven with the aid of these basic assumptions. At the foundation of the various sciences lay certain additional hypotheses which were accepted without proof. Such a hypothesis was termed a postulate. While the axioms were common to many sciences, the postulates of each particular science were different. For Example:
Axiom - Things which are equal to the same thing are also equal to one another(common to many sciences).
Postulate - It is possible to draw a straight line from any point to any other point(particularly in Geometry).
Aristotle by himself used the term “axiom”, which comes from the Greek “axioma”, which means “to deem worth”, but also “to require”. Aristotle had some other names for axioms. He used to call them as “the common things” or “common opinions”. In Mathematics, Axioms can be categorized as “Logical axioms” and “Non-logical axioms”. Logical axioms are propositions or statements, which are considered as universally true. Non-logical axioms sometimes called postulates, define properties for the domain of specific mathematical theory, or logical statements, which are used in deduction to build mathematical theories. “Things which are equal to the same thing, are equal to one another” is an example for a well-known axiom laid down by Euclid.
The term “postulate” is from the Latin “postular”, a verb which means “to demand”. The master demanded his pupils that they argue to certain statements upon which he could build. Unlike axioms, postulates aim to capture what is special about a particular structure. “It is possible to draw a straight line from any point to any other point”, “It is possible to produce a finite straight continuously in a straight line”, and “It is possible to describe a circle with any center and any radius” are few examples for postulates illustrated by EUCLID.