Mathematical Notations#

We largely follow the Machine Learning: The Basics book in terms of notations.

Set Notation#

Table 3 Set Notations#

Notation

Description

aA

This statement indicates that the object a is an element of the set A.

a:=b

This statement defines a to be shorthand for b.

|A|

The cardinality (number of elements) of a finite set A.

AB

A is a subset of B.

AB

A is a strict subset of B.

N

The set of natural numbers 1,2,.

R

The set of real numbers x.

R+

The set of non-negative real numbers x0.

{0,1}

The set consisting of two real-number 0 and 1.

[0,1]

The closed interval of real numbers x with 0x1.

f(),h()

A function or map f() that accepts any element aA from a set A as input and delivers a well-defined element f(a)B of a set B. The set A is the domain of the function f and the set B is the codomain of f. Machine Learning revolves around finding (or learning) a function h (which we call hypothesis) that reads in the features x of a data point and delivers a prediction h(x) for the label y of the data point.

Table 4 Linear Algebra Notations#

Notation

Description

aA

This statement indicates that the object a is an element of the set A.