Set Notation Explained

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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 { }.