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What statement to a theorem can be proven easily using the theorem?
A corollary.
Can a theorem be proven using a corollary?
No, a corollary follows from a theorem that has been proven. Of course, a theorem can be proven using a corollary to a previous theorem.
A corollary is a statement that can be easily proved using the theorem?
Yes, a corollary is a statement that follows readily from a previously proven theorem. It often highlights a specific case or consequence of the theorem, requiring minimal additional proof. Corollaries help to illustrate the broader implications of the original theorem in a concise manner.
Is a corollary a statement that can be proven using a theorem but the proof is usually difficult?
false
True or false a theroem is a statement that can be easily proved?
Neither. A theorem is a proven mathematical statement. This says nothing about how easily it can be proven. e.g. the Pythagorean Theorem is easily proven, but Fermat's Last Theorem is extremely difficult to prove.
What statement to a theorem can be proven easily using the theorem?
A corollary.
Can a theorem be proven using a corollary?
No, a corollary follows from a theorem that has been proven. Of course, a theorem can be proven using a corollary to a previous theorem.
A corollary is a statement that can be easily proved using the theorem?
Yes, a corollary is a statement that follows readily from a previously proven theorem. It often highlights a specific case or consequence of the theorem, requiring minimal additional proof. Corollaries help to illustrate the broader implications of the original theorem in a concise manner.
Is a corollary a statement that can be proven using a theorem but the proof is usually difficult?
false
Is corollary a statement who's proof is typically more involved than a theorem?
No, in fact it is the opposite. A corollary is normally a special case of a theorem and is usually sufficiently important for it to be proven separately from the theorem. This is so that it can then be used in the future. Corollaries follow a theorem and can usually be derived from it very easily.
True or false a theroem is a statement that can be easily proved?
Neither. A theorem is a proven mathematical statement. This says nothing about how easily it can be proven. e.g. the Pythagorean Theorem is easily proven, but Fermat's Last Theorem is extremely difficult to prove.
What can be proven directly from a theorem?
A Corollary
What is a collary?
A corollary is a statement that follows readily from a previously proven statement or theorem. In mathematics, it often refers to a proposition that can be easily derived from an existing theorem without requiring extensive additional proof. Corollaries help to extend the implications of a theorem and can provide further insights or applications of the original result.
Is corollary a statement that is typically more involved than a theorem?
From the start, yes. But once the theorem has been proven it is usually a very minor extra bit.
True or false a theorem is a statement that can be easily proved using colloary?
False. A theorem is a statement that has been proven based on previously established statements, such as axioms and other theorems. A corollary, on the other hand, is a statement that follows readily from a theorem and requires less effort to prove. Thus, theorems are generally more complex and foundational than corollaries.
A collonary is a statement whose proof is typically more involved than theorem?
A corollary is a statement that follows readily from a previously proven theorem, often requiring less effort to prove than the theorem itself. While the theorem provides a broader or more significant result, the corollary often highlights a specific consequence or application of that result. Despite this distinction, the proof of a corollary can still be intricate, depending on the context. In essence, corollaries extend the implications of theorems in a more focused manner.
A statement that can be proven?
theorem
