Final answer:
A paragraph proof in mathematics uses a set of sentences to explain the logical steps needed to reach a conclusion, employing inductive reasoning and often structured like an argumentative essay.
Step-by-step explanation:
A paragraph proof in mathematics utilizes inductive reasoning to substantiate a statement. Contrary to a two-column proof that presents a table of statements alongside their corresponding reasons, a paragraph proof contains a set of sentences that are written in a coherent, logical manner. These sentences explain the steps and reasoning necessary to reach a conclusion, similar to constructing an argument in an essay.
In a paragraph proof, each premise or observation is brought forth as a sentence, linked through logical connectors, leading to a demonstration of the conclusion. This form of proof may start with a topic sentence that outlines the target claim or theorem. Following this, a series of premises or known facts are presented as subsequent sentences. These premises act as the foundational steps towards establishing the claim, built upon through cause-and-effect reasoning. Finally, the proof concludes with analysis and an explanation of how the evidence presented supports the claim, thus demonstrating its validity. By weaving the logical steps into a narrative flow, a paragraph proof provides a structured yet readable argumentative form to convey mathematical proofs.