Proof typically refers to evidence or confirmation that a claim or statement is true or valid. In mathematics, proof is the process of demonstrating the truth of a theorem or proposition through logical reasoning and mathematical symbols. In law, proof refers to the evidence submitted in a trial to establish the guilt or innocence of a defendant. In science, proof is the process of showing that a hypothesis or theory is supported by empirical evidence and can be replicated and validated by others. In general, proof is a vital component of rational inquiry and critical thinking, providing a means to establish knowledge and distinguish fact from fiction.
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