Why do we need this?
I am not sure if you actually need this list but mathematics is everywhere and it’s better to know these notaions. Spacially if you are pursuing higher education or you really want to understand the world you live in. Recently I have started doing mathematics for my Master’s degree and I was having problems remembering some basic mathematical notaions. Which is really bad! So I decided to make a list of some usefull and basic mathematical notaions. I gathered the information mostly from Wikipedia and Quora. I will keep updating the list.
| Notaion | Name | Example | Details |
|---|---|---|---|
| ∈ | is an element of | x ∈ ℕ | x is an element of the set of Natural numbers (ℕ) |
| ∉ | is not an element of | x ∉ ℕ | x is not an element of the set of Natural numbers (ℕ) |
| ℝ | The (set of) real numbers | π ∈ ℝ | π is an element of the set of real numbers |
| ℝn | is the set of all column vectors with n components which are each real numbers | ||
| ℝm×n | is the set of all m×nmatrices whose elements are real numbers. | is the set of all m×n matrices whose elements are real numbers. | |
| ∮ | Contour integral; closed line integral | ||
| | ⟩ | ket vector | |φ⟩ means the vector with label φ; which is in a Hilbert space. | A qubit’s state can be represented as α|0⟩+ β|1⟩; where α and β are complex numbers s.t. |α|2 + |β|2 = 1. |
| ‖...‖ | norm of; length of | ‖ x + y ‖ ≤ ‖ x ‖ + ‖ y ‖ | ‖ x ‖ means the norm of the element x of a normed vector space. |
| ⌊...⌋ | floor of | ⌊4⌋ = 4; ⌊2.1⌋ = 2; ⌊2.9⌋ = 2; ⌊−2.6⌋ = −3 | ⌊x⌋ means the floor of x; i.e. the largest integer less than or equal to x. |
| ⌈...⌉ | ceiling | ⌈4⌉ = 4; ⌈2.1⌉ = 3; ⌈2.9⌉ = 3; ⌈−2.6⌉ = −2 | ⌈x⌉ means the ceiling of x; i.e. the smallest integer greater than or equal to x. |
| â | “Pronounced ““a hat””” | â is the normalized version of vector a; having length 1. | |
| ℤ | ℤ means both positive and negative integers. | ||
| ℤ+ or ℤ> | ℤ+ or ℤ> means positive integers (0 not included) | ||
| ℤ≥ | ℤ≥ means positive integers including 0 | ||
| { : } { | } | “set builder notation, the set of ... such that” | {x : P(x)} means the set of all x for which P(x) is true.{x | P(x)} is the same as {x : P(x)}. | {n ∈ ℕ : n2 < 20} = { 1, 2, 3, 4 } |
