write the difference between an axiom and a postulate with an example
Answers
Answered by
7
hey mate....!
here is your answer
In Geometry, "Axiom" and "Postulate" are essentially interchangeable. In antiquity, they referred to propositions that were "obviously true" and only had to be stated, and not proven. In modern mathematics there is no longer an assumption that axioms are "obviously true". Axioms are merely 'background' assumptions we make. The best analogy I know is that axioms are the "rules of the game". In Euclid's Geometry, the main axioms/postulates are:
Given any two distinct points, there is a line that contains them.Any line segment can be extended to an infinite line.Given a point and a radius, there is a circle with center in that point and that radius.All right angles are equal to one another.If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. (Theparallel postulate).
A theorem is a logical consequence of the axioms. In Geometry, the "propositions" are all theorems: they are derived using the axioms and the valid rules. A "Corollary" is a theorem that is usually considered an "easy consequence" of another theorem. What is or is not a corollary is entirely subjective. Sometimes what an author thinks is a 'corollary' is deemed more important than the corresponding theorem. (The same goes for "Lemma"s, which are theorems that are considered auxiliary to proving some other, more important in the view of the author, theorem).
A "hypothesis" is an assumption made. For example, "If xx is an even integer, then x2x2 is an even integer" I am not asserting that x2x2 is even or odd; I am asserting that ifsomething happens (namely, if xxhappens to be an even integer) thensomething else will also happen. Here, "xx is an even integer" is the hypothesis being made to prove it
hope it may help you
Thank you
here is your answer
In Geometry, "Axiom" and "Postulate" are essentially interchangeable. In antiquity, they referred to propositions that were "obviously true" and only had to be stated, and not proven. In modern mathematics there is no longer an assumption that axioms are "obviously true". Axioms are merely 'background' assumptions we make. The best analogy I know is that axioms are the "rules of the game". In Euclid's Geometry, the main axioms/postulates are:
Given any two distinct points, there is a line that contains them.Any line segment can be extended to an infinite line.Given a point and a radius, there is a circle with center in that point and that radius.All right angles are equal to one another.If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. (Theparallel postulate).
A theorem is a logical consequence of the axioms. In Geometry, the "propositions" are all theorems: they are derived using the axioms and the valid rules. A "Corollary" is a theorem that is usually considered an "easy consequence" of another theorem. What is or is not a corollary is entirely subjective. Sometimes what an author thinks is a 'corollary' is deemed more important than the corresponding theorem. (The same goes for "Lemma"s, which are theorems that are considered auxiliary to proving some other, more important in the view of the author, theorem).
A "hypothesis" is an assumption made. For example, "If xx is an even integer, then x2x2 is an even integer" I am not asserting that x2x2 is even or odd; I am asserting that ifsomething happens (namely, if xxhappens to be an even integer) thensomething else will also happen. Here, "xx is an even integer" is the hypothesis being made to prove it
hope it may help you
Thank you
GalankiSupriya:
mark it as brainliy answer okay
ok
Tq very much
Thank you
Answered by
2
axioms are obvious statements which don't need proof
whereas postulates need proof
ex halves of equals are equal is very obvious that u can believe wd out proof but to know whether a st line can be drawn from any point to any other point u need to check it out in order to believe it
whereas postulates need proof
ex halves of equals are equal is very obvious that u can believe wd out proof but to know whether a st line can be drawn from any point to any other point u need to check it out in order to believe it
Thank u
Similar questions