what is the difference between axioms & postulates

 

Hi !
 
Axioms and postulates are essentially the same thing. These are mathematical truths those are accepted without proof.
 
Axioms are generally statements made about real numbers. For example, for any two real numbers a and b, a + b = b + a.
Often axioms holds true for geometric figures, and since real numbers are an important part of geometry when it comes to measuring figures, axioms are very useful.
 
 Postulates are generally more geometry-oriented. They are statements about geometric figures and relationships between different geometric figures.
 
Hope! This will help you.

 

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In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered to be either self-evident, or subject to necessary decision. In other words, an axiom is a logical statement that is assumed to be true. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths.

In mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". In both senses, an axiom is any mathematical statement that serves as a starting point from which other statements are logically derived. Unlike theorems, axioms (unless redundant) cannot be derived by principles of deduction, nor are they demonstrable by mathematical proofs, simply because they are starting points; there is nothing else from which they logically follow (otherwise they would be classified as theorems).

Logical axioms are usually statements that are taken to be universally true (e.g., A and B implies A), while non-logical axioms (e.g., a + b = b + a) are actually defining properties for the domain of a specific mathematical theory (such as arithmetic). When used in the latter sense, "axiom," "postulate", and "assumption" may be used interchangeably. In general, a non-logical axiom is not a self-evident truth, but rather a formal logical expression used in deduction to build a mathematical theory. 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). There are typically multiple ways to axiomatize a given mathematical domain.

Outside logic and mathematics, the term "axiom" is used loosely for any established principle of some field......!!!!

They have no difference in between them ok....!!!!!

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 An axiom is in some sense thought to be strongly self-evident. A "postulate," on the other hand, is simply postulated, e.g. "let" this be true. There need not even be a claim to truth, just the notion that we are going to do it this way and see what happens.

hope so this help u..

thumbs up plz

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