Introduction
This page contains Math symbols and basic concepts that you may need when studying the concepts on this site, especially if you are unfamiliar or rusty at math.
Math Symbols
The following symbols are contained on this site. This list will help you better understand the symbols’ meanings and usages.
≡ – is equivalent to: (a is equivalent to b) or (a ≡ b)
> – greater than: (x greater than y) ≡ (x > y)
≥ – greater than or equal: (x greater than or equal to y) ≡ (x ≥ y)
< - less than: (x less than y) ≡ (x < y)
≤ – less than or equal to: (x less than or equal to y) ≡ (x ≤ y)
= – equal: (x equals y) ≡ (x = y)
≠ – not equal: (x not equal to y) ≡ (x ≠ y)
∅ – Null or empty set: (Α is a null set) ≡ (Α = ∅)
∈ – set membership: (x is in Α) ≡ (x ∈ Α)
∉ – set non-membership: (x is not in Α) ≡ (x ∉ Α)
∪ – set union: (x ∈ Α or Β) ≡ (x ∈ Α ∪ Β)
∩ – set intersection: (x ∈ Α and Β) ≡ (x ∈ Α ∩ Β)
Σ – Summation: (1 + 2 + 3 + 4) ≡ (Σ(x=1 to 4) x)
Sets
Sets are groups of elements that can be in finite, finite, or null. A null set has no elements. For example:
Α = {x,y,z}. Β = {w,x,y}. The null or empty set ∅ = {}.
A finite set can have 0,1,2 or more elements. The cardinality of a set is a count of the total number of elements.
Cardinality of set Α = |Α| = 3
A set contains members, and the question of whether element ‘x’ is in set Α. The way to state set membership symbolically is as follows:
The element x is a member of set Α ≡ (x ∈ Α)
The element x is not a member of set Α ≡ (x ∉ Α)
The union of two sets is the combined set containing elements from one set or the other. The intersection of two sets is the combined set containing elements from one set and the other.
The union of Α and Β ≡ Α ∪ Β = {w,x,y,z}.
The intersection of Α and Β ≡ Α ∩ Β = {x,y}.
Calculations
Factorials are an important part of calculating the number of permutations in a set. So a short explanation is appropriate. Let N be a positive number. Then:
N-factorial or N! = N ⋅ (n-1) ⋅ N-2) ⋅ … ⋅ 1
0! = 1, by definition.
3! = 3*2*1 = 6
Math Concepts
Math induction is a method of proving that a formula or concept tied to an integer applies to all integers starting at a minimum value, usually 0 or 1.
First show that the concept is true for N = 0 (or a minimum value).
Then assume the concept is true for the integer N and show it is true for integer N + 1.
The concept is then true for all values of N ≥ 0 (or the minimum value).