Lab-1 Intervals and Equations(1).pptx

Lab-1 Intervals and Equations(1).pptx - SETS OF REAL...

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SETS OF REAL NUMBERS Hallmark University
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NUMBER TYPES Natural Numbers are the numbers we use in counting: {1, 2, 3, 4, 5, 6, 7, …} Whole Numbers are the natural number plus 0: {0, 1, 2, 3, 4, 5, 6, 7, …} Integers are the whole numbers and their negatives: {… , -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, …} Rational Numbers are fractions that have an integer numerator and a non zero denominator. Their decimals are either terminating or repeating decimals. {6, 0.125, 1.3333…, -0.454545…} Irrational Numbers are like Rational Numbers but are either non- terminating or non-repeating. {∏, 22/7, 1.01001000100001…}
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Unbound Intervals (a, ∞) x > a ( (2, ∞) x > 2 | ( 2 a -∞ [a, ∞) x ≥ a [ a [a, ∞) x ≥ 3 | [ 3 (-∞, ∞) x > -∞ 0 0
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Unbound Intervals -∞ (-∞, a) x < a ) a -∞ (-∞, -2) x < -2 ) | -∞ 0 -2 0 (-∞, a] x ≤ a ] (-∞, 4) x ≤ 4 | ] -∞ 4 a
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Open Intervals and Half-Open Intervals (a, b) a < x < b ( ) a (-2, 4) -2 < x < 4 ( | ) 0 -2 0 (a, b] a < x ≤ a ( ] (2, 4] 2 < x ≤ 4 | ( ] 2 b b 4 a 4 OPEN HALF-OPEN
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Half-Open Intervals and Closed Intervals b [a, b) a ≤ x < b [ ) [-3, 2) -3 ≤ x < 2 [ | ) [a, b] a ≤ x b [ ] [a, b] -3 ≤ x -1 [ ] | a 0 b a -3 0 2 -1 -3 HALF-OPEN CLOSED
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Union and Intersecting Intervals [-3, 1) U (3, 5] -3 ≤ x < 1 and 3 < x ≤ 5 [ | ) ( ] -3 5 3 1 0 Union: Intersection : -∞ | ( ] 0 -2.5 2 (- , 2] (-2.5, ) x ≤ 2 and x > -2.5 -2.5 < x ≤ 2 U
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Absolute Value
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Absolute Value Equations Write the expression without using absolute value symbols. |x + 1| and x ≥ 2 Since x + 1 will always be positive, |x + 1|= x + 1 |x + 1| and x ≤ 2 Since x + 1 will always be negative, |x + 1|= (x + 1) |x 7| and x > Since x + 1 will always be positive, |x + 1|= x 7
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Polynomials Monomial or Term Coefficient Base Exponent
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