## Elementary Math Chapter 8.1 Trues and Falses

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Bodereca  on February 20, 2011

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# Elementary Math Chapter 8.1 Trues and Falses

 Every Whole number is an integerTRUE
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#### Definitions

Every Whole number is an integer TRUE
The set of additive inverses of the negative integers is a proper subset of the whole numbers TRUE
The set of additive inverses of the whole numbers is equal to the set of integers FALSE
0, -1 , -2, -3, -4 PLUS all the whole numbers make a set of integers
Every integer is a Whole Number FALSE
Every whole number is an integer { 0, 1, 2, 3,...}
Write in words 5 - 2
five minus two
Write in words - 6
opposite of 6
negative 6
write in words - 3
opposite of 3
negative 3
Absolute Value The absolute value of an integer a, written ⌉a⌉, is defined to be the distance from a to zero on the integer number line.
⌉3⌉ = 3
⌉0⌉ = 0
⌉-7⌉ = 7
absolute value examples ⌉5⌉ - ⌉7⌉ = 5 - 7 = 2
absolute value examples - ⌉ 7 - 5⌉ = - ⌉2⌉ = - 2
absolute value examples ⌉- (7-5)⌉ = ⌉-2⌉ = 2
Closure property for subtraction of integers HOLDS - 3 - 7 is an integer
Commutative property DOES NOT HOLD for subtraction NO; 3 -2 ≠ 2 - 3
Associative property DOES NOT HOLD for subtraction NO ; 5 - (4 - 1) ≠ (5 - 4) -1
Identity property DOES NOT HOLD for subtraction NO; 5 - 0 ≠ 0 - 5
a - b = c a - b = c
a + (-b) = c
a + (-b) (+b) = c + b
a = b + c
i.pair that satisfies ⌉a + b⌉ = ⌉a⌉ + ⌉b⌉
When a and b have the same sign or when one or both are 0
ii. Pair that satisfies ⌉a + b ⌉ 〈 ⌉a⌉ + ⌉b ⌉
When a and b are nonzero and have opposite signs
iii. pair that satisfies ⌉a + b ⌉ 〉 ⌉a⌉ + ⌉b⌉
Never
iv. pair that satisfies ⌉a + b ⌉ ≤ ⌉a⌉ + ⌉b⌉
All integers will work

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