Elementary Math Chapter 8.1 Trues and Falses
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20 terms
Terms | 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 additive inverse of 6 negative 6 |
| write in words | - 3 opposite of 3 additive inverse 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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