Quick Answer: What Is A Corollary Statement?

What does corollary mean?

1 : a proposition (see proposition entry 1 sense 1c) inferred immediately from a proved proposition with little or no additional proof.

2a : something that naturally follows : result … love was a stormy passion and jealousy its normal corollary.—.

Do corollaries require proof?

Corollary — a result in which the (usually short) proof relies heavily on a given theorem (we often say that “this is a corollary of Theorem A”). Proposition — a proved and often interesting result, but generally less important than a theorem. … Axiom/Postulate — a statement that is assumed to be true without proof.

How do you use the word obloquy in a sentence?

For many years she had much obloquy to endure. Terrified by the storm of obloquy which he aroused, he fled from office. for the means of heaping obloquy on all who supported the established institutions of the country.”

Is a theorem accepted without proof?

A theorem is a statement in geometry that is accepted without proof.

How do you use corollary in a sentence?

It is a necessary corollary to enable an adoption to take place. Looking forward Looking forward is the obvious corollary to looking back. Science museums were a natural corollary to all these.

What is the difference between a theorem and a proof?

proofA proof is a series of true statements leading to the acceptance of truth of a more complex statement. is the hypotenuse of the triangle. theoremA theorem is a statement that can be proven true using postulates, definitions, and other theorems that have already been proven.

What is the difference between corollary and Theorem?

a theorem is a more important statement than a proposition which says something definitive on the subject, and often takes more effort to prove than a proposition or lemma. A corollary is a quick consequence of a proposition or theorem that was proven recently.

What is a corollary in psychology?

Commonality Corollary: To the extent that one person employs a construction of experience which is similar to that employed by another, his psychological processes are similar to those of the other person.

Are axioms accepted without proof?

axiom, in mathematics and logic, general statement accepted without proof as the basis for logically deducing other statements (theorems). … The axioms should also be consistent; i.e., it should not be possible to deduce contradictory statements from them.

How do I prove a corollary?

A Corollary could be described as a “post-proof.” A corollary is something that follows almost obviously from a theorem you’ve proved. You work to prove something, and when you’re all done, you realize, “Oh my goodness! If this is true, than [another proposition] must also be true!”

What is a theorem example?

A result that has been proved to be true (using operations and facts that were already known). Example: The “Pythagoras Theorem” proved that a2 + b2 = c2 for a right angled triangle. A Theorem is a major result, a minor result is called a Lemma. …

What is difference between Axiom and Theorem?

The axiom is a statement which is self evident. But,a theorem is a statement which is not self evident. An axiom cannot be proven by any kind of mathematical representation. … A theorem can be proved or derived from the axioms.

What is a lemma in proof?

Lemma: A true statement used in proving other true statements (that is, a less important theorem that is helpful in the proof of other results). … Proof: The explanation of why a statement is true. • Conjecture: A statement believed to be true, but for which we have no proof.

What is difference between Lemma and Theorem?

There is no formal distinction between a lemma and a theorem, only one of intention (see Theorem terminology). However, a lemma can be considered a minor result whose sole purpose is to help prove a theorem – a step in the direction of proof – or a short theorem appearing at an intermediate stage in a proof.

What is a logical corollary?

a judgment (statement, proposition, formula) that is the logical result of, or in other words, follows logically from the premises of a conclusion or from the premises of an inference consisting of a series of conclusions; that which can be inferred from the premises on the basis of the rules and laws of logic.

What is called Theorem?

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general principle that makes it part of a larger theory. The process of showing a theorem to be correct is called a proof.