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15 Cards in this Set
- Front
- Back
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What is another word for demonstrandum?
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theorem
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What does Q.E.D. stand for?
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quod erat demonstrandum
"which was to be demonstrated" |
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What is the associative property?
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We say that an operation is Associative (or that it has the Associative Property) if, when performing the operation on three numbers in a given order, it does not matter if one performs the operation on the first two numbers first, or on the last two numbers first.
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What property is the following an example of?
(a + b) + c = a + (b + c) |
associative property
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What is the commutative property?
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We say that an operation is Commutative (or that it has the Commutative Property) if it always produces the same answer when exchanging the two given quantities.
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What property is the following an example of?
a + b = b + a |
commutative property
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Is subtraction commutative?
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No, subtraction is NOT commutative.
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Is subtraction associative?
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No, subtraction is NOT associative.
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What is the first step to writing a proof?
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Write down what you are going to prove.
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What is the second step to writing a proof?
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Write the word "Proof" after the statement you are going to prove.
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How do you end a proof?
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Write Q.E.D. at the end.
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How do you quote axioms or therorems?
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Only quote the part that is needed to prove what you need to prove. Do NOT fully quote them.
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How do you quote definitions in a proof?
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Only use the part of the definition that you need for your proof. Do NOT fully quote definitions.
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What should you use to make proofs easier?
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Use letters to denote numbers and rephrase the statement you are trying to prove in terms of those letters instead of numbers.
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How should you justify your statements?
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Every statement you make should follow from a definition, an axiom, a theorem, or reasoning. You must say why each statement is true either before or after the statement.
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