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26 Cards in this Set
- Front
- Back
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When does a number measure another number?
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A number measures another number if, being repeated a number of times, it equals the other number. We also say that the first number divides the other number, or that it is a divisor of the other number.
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When is a number a multiple of another number?
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A number is a multiple of another number if it is measured by it.
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How do we classify the parts of a whole?
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We classify the parts of a whole into aliquot and aliquant parts.
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What are aliquot parts?
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Aliquot parts are the parts that measure the whole.
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What are aliquant parts?
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Aliquant parts are the parts that DO NOT measure the whole.
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Theorem 3
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If a number measures another number, it will also measure all the numbers which that other number measures.
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If a number measures another number, it will also measure all the numbers which that other number measures.
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Theorem 3
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A greater number cannot measure a smaller number.
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Theorem 4
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Theorem 4
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A greater number cannot measure a smaller number.
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Law of Trichotomy
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When comparing two numbers, one (and only one) of the following three possibilities must be true: either the first one is smaller than the second one, or they are equal, or the first one is greater than the second one.
i.e., given two numbers a and b, either a < b, or a = b, or a > b. |
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Given two numbers a and b, either a < b, or a = b, or a > b.
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Law of Trichotomy
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Since a > b, a cannot measure b.
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Theorem 4
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Since a measures b, a will also measure all the numbers that b measures.
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Theorem 3
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a measures c and c measures b ---> a measures b
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Theorem 3
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a is an aliquot part of b ---> a measures b
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Definition of an Aliquot part
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a is a multiple of b ---> a is measured by b
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Definition of a Multiple
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a > b ---> a does not measure b
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Theorem 4
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a < b ---> a is not equal to b
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Law of Trichotomy
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Never quote definitions word for word in a proof.
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True
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Always quote definitions word for word in a proof.
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False.
Only use the part or parts that you need. |
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Always justify every statement of a proof.
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True
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Never fully quote axioms in a proof.
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True
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Always fully quote axioms in a proof.
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False.
Only quote the part or parts that you need. |
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Always use letters to denote numbers when writing proofs.
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False.
Letters can be helpful, but you do not always have to use them. |
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Always use "By the definition of...." when using definitions in a proof.
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False.
Most statements regarding a definition can be written in the form "Since... then...." |
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Always fully restate the statement of the theorem before writing Q.E.D. when ending a proof.
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False.
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