HELLO FRIENDS! im about to teach you how to read more math! today's lesson is set notation. these symbols are used a lot in mathematical writing because it helps us save space when describing sets, and you need to understand them when they appear. alright here we go:
symbol: { }
meaning: "set", "a collection of elements"
example: A = {3, 7, 9, 14}, B = {9, 14, 28}
symbol: A ∩ B
meaning: "intersection", "objects that belong to set A and set B"
example: A = {3, 7, 9, 14}, B = {9, 14, 28}, A ∩ B = {9, 14}
symbol: A ∪ B
meaning: "union", "objects that belong to set A or set B"
example: A = {3, 7, 9, 14}, B = {9, 14, 28}, A ∪ B = {3, 7, 9, 14, 28}
symbol: A ⊆ B
meaning: "subset", "A is a subset of B. set A is included in set B."
examples: {9, 14, 28} ⊆ {9, 14, 28} and {9, 14} ⊆ {9, 14, 28}
symbol: A ⊂ B
meaning: "proper subset", "A is a subset of B, but A is not equal to B."
example: {9, 14} ⊂ {9, 14, 28}
note: {9, 14, 28} ⊂ {9, 14, 28} would be FALSE because they are equal sets
symbol: A\B or A-B
meaning: "relative complement", "objects that belong to A and not to B"
example: A = {3, 9, 14}, B = {1, 2, 3}, A-B = {9, 14}
symbol: |A|
meaning: "cardinality", "the number of elements of set A"
example: A = {3, 9, 14}, |A| = 3
symbol: P(A)
meaning: "power set", "all subsets of A"
example: A = {1, 2}, P(A) = {{}, {1}, {2}, {1, 2}}
there are also sets of numbers that are used so often that they have special names and symbols
symbol: ℕ
common set: the natural numbers
description: the whole numbers from 1 upwards (or from 0 upwards in some fields of mathematics) aka the set {1, 2, 3, ...}
symbol: ℤ
common set: integers
description: the positive whole numbers, negative whole numbers, and 0 aka the set {..., -3, -2, -1, 0, 1, 2, 3, ...}
symbol: ℚ
common set: rationals
description: the set of all numbers you can make by dividing one integer by another (but not dividing by 0)
symbol: ℝ
common set: real numbers
description: ANY value on the number line, can be positive, negative, or zero.
symbol: ℂ
common set: complex numbers
description: a combination of a real and imaginary number in the form a+bi, where a and b are real, and i is imaginary
symbol: ∅
common set: the empty set
description: self explanatory. its an empty set aka { }.