corollary
In mathematics, a corollary is a statement that follows from and is immediate to a previously proven or stated theorem
In mathematics, a corollary is a statement that follows from and is immediate to a previously proven or stated theorem. Essentially, a corollary is a result that can be easily derived or inferred from a known result or theorem. It is typically a smaller or less significant consequence of a more general or important result.
Corollaries serve to further expand our knowledge and understanding of mathematical concepts. They provide additional insights and applications of the main theorem, and often simplify complex ideas by presenting them in a more specific or specialized context.
When proving a theorem, mathematicians may often encounter several smaller results or observations along the way. These smaller results are often classified as corollaries. They are considered to be “obvious” or “direct” consequences of the main theorem and are usually stated and proved immediately after the main theorem.
Corollaries are valuable in mathematics as they help establish connections between different areas of study, highlight important implications of known theorems, and provide a stepping stone for further research and exploration in a specific field of mathematics.
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