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bok:maths:set-notation
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bok:maths:set-notation [2021/07/30 14:00] anwlur created |
bok:maths:set-notation [2021/07/30 14:53] (current) anwlur [Notation] |
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| + | ====== Notation ====== | ||
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| Consider a Universal set of (U) = {1, 3, 5, 8, 10, 35, 36, 37} | Consider a Universal set of (U) = {1, 3, 5, 8, 10, 35, 36, 37} | ||
| * {}; set; A collection of elements; (A) = {1, 3, 5, 8}, (B) = {5, 8, 10, 35}, (C) = {8, 10, 36, 37} | * {}; set; A collection of elements; (A) = {1, 3, 5, 8}, (B) = {5, 8, 10, 35}, (C) = {8, 10, 36, 37} | ||
| + | * a ∈ A; element of; Element a is a member of set A; 3 ∈ {1, 3, 5, 8} | ||
| + | * a ∉ A; negation of a ∈ A | ||
| + | * ∀; for all; ∀ x, P(x) means P(x) is true for all of x | ||
| + | * ∃; existential quantification; ∃ x : P(x) means there exists at least one x such that P(x) is true | ||
| + | * ∃!; uniqueness quantification; ∃! x : P(x) means there exists exactly one x such that P(x) is true | ||
| * A ∪ B; union; Elements that belong to A or B; A ∪ B = {1, 3, 5, 8, 10, 35} | * A ∪ B; union; Elements that belong to A or B; A ∪ B = {1, 3, 5, 8, 10, 35} | ||
| * A ∩ B; intersection; Elements that belong to A and B; A ∩ B = {5, 8} | * A ∩ B; intersection; Elements that belong to A and B; A ∩ B = {5, 8} | ||
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| * A ⊃ B; proper superset; Every element of B is also an element of A but B ≠ A; {1, 3, 5, 8, 10, 35} ⊃ {1, 3} | * A ⊃ B; proper superset; Every element of B is also an element of A but B ≠ A; {1, 3, 5, 8, 10, 35} ⊃ {1, 3} | ||
| * A \ B or A - B; relative complement; Elements that are members to A but not members to B; A - B = {1, 3} | * A \ B or A - B; relative complement; Elements that are members to A but not members to B; A - B = {1, 3} | ||
| - | <math> A^c <\math> Ac = complement | + | * A' or A^c or A with bar over the top; complement; Every element in Universal set but not in A; A^c = {10, 35, 36, 37} |
| * {} or Ø; null set or empty set; A set with no elements; | * {} or Ø; null set or empty set; A set with no elements; | ||
| * P(A); power set; Given a set A, power set of A is the set of all subsets of the set; P({a, b}) = {Ø, {a}, {b}, {a,b}} | * P(A); power set; Given a set A, power set of A is the set of all subsets of the set; P({a, b}) = {Ø, {a}, {b}, {a,b}} | ||
| + | * A Δ B; symmetric difference; Element that are in A or B but not members of the intersection of A and B; A Δ B = {1, 3, 10, 35} | ||
| + | * |A| or #A; cardinality; Number of elements of set A; |A| = 4 | ||
| + | * A x B; cartesian product; Set of all ordered pairs from A and B; {1,2} x {3,4} = {(1,3), (1,4), (2,3), (2,4)} | ||
| + | * ℵ; natural numbers, positive whole numbers | ||
| + | * Z; integers, negative or positive whole numbers and zero | ||
| + | * R; real numbers; R = {x : -∞ < x < ∞} | ||
| + | * →; to; f : X → Y means function f maps the set X into set Y | ||
| + | * |→; maps to f :x |→ y means function f maps the element x to the element y | ||
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| + | ====== Set Builder Notation ====== | ||
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| + | A = {x : x ∈ ℵ} the set A is equal to a set of x such that (| can also be used) x are elements of N (Natural numbers) | ||
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| + | ====== Arithmetic ====== | ||
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| + | * n(A ∪ B) = n(A) + n(B) – n(A ∩ B) | ||
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bok/maths/set-notation.1627653628.txt.gz · Last modified: 2021/07/30 14:00 by anwlur
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