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Math: unit 1 > 7. Axioms+ 8.Applications > Flashcards

7. Axioms+ 8.Applications Flashcards

1
Q

Axioms

A

Statements about mathematics that are accepted without proof

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2
Q

Theorems

A

Statements about mathematics requiring proof; starts from axioms and follows a logical path to the theorem you wanna prove.

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3
Q

Closure axiom?

A

Given a set and an operation, we say that a set has closure for that operation if we can guarantee that the result of performing that operation on any elements in the set will result in another element of that same set.

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4
Q

Closure axiom for wholes?

A

Addition and multiplication are closed. Subtraction and division are not

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5
Q

Closure axiom for integers?

A

Addition, multiplication, and subtraction are closed. Division is not.

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6
Q

Closure axiom for reals?

A

Addition, multiplication, subtraction, and division are all closed.

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7
Q

a=a

A

Reflexive property

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8
Q

If a=b then b=a

A

Symmetric property

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9
Q

If a=b and b=c, then a=c

A

Transitive property

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10
Q

Commutative property of addition?

A

a+b=b+a

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11
Q

Associative property of addition?

A

a+(b+c)=(a+b)+c

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12
Q

Identity property of addition?

A

a+o=a

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13
Q

Commutative property of multiplication?

A

a(b)=b(a)

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14
Q

Associative property of multiplication?

A

A(bc)=(ab)c

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15
Q

Identity property of multiplication?

A

a*1=a

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16
Q

Multiplicative inverse?

A

a*1\a=1;a not equal to 0

17
Q

Distributive property

A

a(b+c)=(ab)+(ac)

18
Q

Zero property?

A

a*o=o

19
Q

General properties?

A

Reflexive
Symmetric
Transitive

20
Q

Properties of addition?

A

Commutative
Associative
Identity
Additive inverse

21
Q

Properties of multiplication?

A 
Commutative
Associative
Identity
Multiplicative inverse
Distributive
Zero
22
Q

Additive inverse property?

A

a+(-a)=0

23
Q

To find the value of a multi-step arithmetic expression?

A

A definite order of operations must be followed

24
Q

Order of operations?

A 
Parenthesis
Exponents
Multiplication
Division from left to right
Addition
Subtraction from left to right
25
Q

Why does a proof need axioms to build on?

A

A proof needs axioms to build on otherwise the proof would have nothing to be based off of

26
Q

How can axioms about addition in particular be helpful in developing theorems about multiplication?

A

Because multiplication is just repeated addition

27
Q

How can axioms about addition in particular be helpful in developing theorems about multiplication?

A

Because multiplication is just repeated addition

Math: unit 1 (9 decks)

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