Write differences between axioms and postulates?
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Answer:
Axioms and Postulates.
A statement, usually considered to be true without proof (that is, something which is self-evident) is said to be an axiom.
We mostly use axioms at the starting point in mathematical proofs for deducing other truths.
Initially, axioms and postulates were treated as two different things.
'Postulate' refers to a hypothesis that is specific to a certain line of inquiry, that is accepted without proof; they are simply taken as given.
But, in modern mathematics, these two terms are used with not much difference in meaning, their role is very similar to that of undefined terms.
A postulate can be specific on a particular field while an axiom generally is true for any field in science.
Sometimes non-logical axioms are referred to as postulates. They are the fact based on reasoning. Lemma and theorems can be derived with the help of postulates.
Postulates can be considered as statements about geometric figures and relationships between different geometric figures, hence they are generally more geometry-oriented.
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.
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