1 Step Proofs

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What is a one-step proof?

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A one-step proof is a logical argument that demonstrates the truth of a statement using a single step or operation, often involving algebraic manipulation or a simple geometric property.

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What is the purpose of a proof in mathematics?

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The purpose of a proof is to provide a logical and convincing argument that a mathematical statement is true, ensuring that conclusions are based on established principles and definitions.

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Define 'theorem'.

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A theorem is a statement that has been proven to be true based on previously established statements, such as other theorems, axioms, and definitions.

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What is an axiom?

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An axiom is a statement or proposition that is regarded as being self-evidently true, serving as a starting point for further reasoning and arguments.

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Explain the term 'conjecture'.

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A conjecture is an unproven statement or hypothesis that is believed to be true based on observations or patterns.

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What does it mean to justify a step in a proof?

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To justify a step in a proof means to provide a logical reason or explanation for why that step is valid, often referencing definitions, theorems, or properties.

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What is a counterexample?

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A counterexample is an example that disproves a conjecture or statement, showing that it is not universally true.

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How do you write a conclusion in a proof?

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A conclusion in a proof summarizes the result that has been established, often restating the theorem or statement that has been proven.

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What is the difference between a direct proof and an indirect proof?

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A direct proof demonstrates the truth of a statement by straightforward logical deductions, while an indirect proof (or proof by contradiction) assumes the opposite of the statement and shows that this assumption leads to a contradiction.

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What is a geometric proof?

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A geometric proof is a logical argument that uses geometric concepts, figures, and properties to demonstrate the truth of a geometric statement.