What is the meanings of the words lemma, theorem, axioms,corollary, theory.differentiate
What is the meanings of the words lemma, theorem, axioms,corollary, theory.differentiate
Axioms or postulates: A set of statement without proof which is assumed to be true and used building blocks to prove several mathematical theorems and results.
A theorem is a proven proposition. (A proposition is a mathematical statement that is either true or false) .A theorem is a result that can be proven to be true from a set of axioms.An example of a theorem is Pythagoras Theorem, stating for every right triangle with leg lengths aa and bb, and hypotenuse cc, then the relation a2+b2=c2a2+b2=c2 always holds true.
A theory is a set of ideas used to explain why something is true, or a set of rules on which a subject is based on.
A corollary is a result from a theorem that doesn’t require too much proof to show. An example of this can be seen here:
Theorem: A triangle is isosceles iff two angles in a triangle are congruent.
Corollary: An equilateral triangle is equiangular.
A lemma is a theorem that is proven in a proof to help derive the next result. An example of this is below:
Problem: Find and prove all primes p that divide N=2^100⋅3^23.
Lemma: If prime p divides integer ab, then pp divides a or p divides b.
The above lemma would help simplify the problem greatly.
Hope this helps :)
Axioms or postulates: A set of statement without proof which is assumed to be true and used building blocks to prove several mathematical theorems and results.
A theorem is a proven proposition. (A proposition is a mathematical statement that is either true or false) .A theorem is a result that can be proven to be true from a set of axioms.An example of a theorem is Pythagoras Theorem, stating for every right triangle with leg lengths aa and bb, and hypotenuse cc, then the relation a2+b2=c2a2+b2=c2 always holds true.
A theory is a set of ideas used to explain why something is true, or a set of rules on which a subject is based on.
A corollary is a result from a theorem that doesn’t require too much proof to show. An example of this can be seen here:
Theorem: A triangle is isosceles iff two angles in a triangle are congruent.
Corollary: An equilateral triangle is equiangular.
A lemma is a theorem that is proven in a proof to help derive the next result. An example of this is below:
Problem: Find and prove all primes p that divide N=2^100⋅3^23.
Lemma: If prime p divides integer ab, then pp divides a or p divides b.
The above lemma would help simplify the problem greatly.
Hope this helps :)
