The structure of mathematical proofs

Mathematical proofs are structured arguments that demonstrate the truth of a mathematical statement. They typically follow a logical sequence, starting with definitions and known facts. A proof begins with a clear statement of what is being proven, followed by a series of logical steps that build on each other, leading to a conclusion. Each step must be justified, using previous results, axioms, or logical reasoning. The goal is to provide a convincing demonstration that leaves no room for doubt, ensuring the reader can follow and understand why the statement holds true.