Corollary
A corollary is a statement that can be easily deduced or derived from a previously proven or accepted proposition or theorem
A corollary is a statement that can be easily deduced or derived from a previously proven or accepted proposition or theorem. It is a kind of logical consequence or extension of the main result. Corollaries are often used to further clarify or strengthen the implications of a theorem.
Corollaries provide additional information or results that follow naturally from the original theorem. They often arise as an immediate consequence of the proof or by applying specific conditions to the theorem. In other words, if the main theorem is true, then the corollary must also be true.
Corollaries are useful in mathematics because they help establish connections and provide further insights into the main ideas and theories. They can also help simplify complex arguments by breaking them down into more manageable components.
When presenting a proof, mathematicians often include corollaries to offer a broader perspective or to showcase the range of consequences arising from a particular theorem. While corollaries are not as significant as theorems themselves, they play a crucial role in the development and understanding of mathematical concepts.
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