Lesson 3-4 | MIDTERMS | MathWorld

Pattern

defined as: regular, repeated, recurring forms of design, etc.

Sequence

is a function whose domain is the set of positive integers and an ordered list of numbers.

Infinite

its domain is the set of positive integers without a last term {1, 2, 3, 5, …}.

Finite

its domains is the set of positive integers {1, 2, 3, 5, …, n} which has a last term, n.

Term

each number in a sequence.

Arithmetic Sequence

is a type of sequence whose term after the 1^st term is obtained by adding a constant number to the preceding term.

Geometric Sequence

is a type of sequence whose term after the 1st term is obtained by multiplying a constant number to the preceding term.

Common Ratio

constant number in a geometric sequence.

Fibonacci Sequence

is a type of sequence in which first few terms are identified and the succeeding terms are obtained by adding these first few terms that are already defined.

Series

is the sum of the terms of a sequence.

Leonardo Pisano

He introduced wide-ranging mathematical concepts as what is known as the Arabic numbering system, the concept of square roots, number sequencing such as the Fibonacci Sequence.

Fibonacci Sequence

was discovered after an investigation on the reproduction of rabbits.

The Golden Ratio

is often denoted by the Greek letter p (Phi). This is approximately equal to 1.618

Language

is a system of communication which consists of a set of sounds and written symbols which are used by the people of a particular country or region for talking of writing.

Language of Mathematics

is a system used by mathematicians to express, communication mathematical ideas, concepts, and theories.

PRECISE

able to make very fine distinctions

CONCISE

able to say things briefly

POWERFUL

able to express complex thoughts with relative ease

Ten-Digit

In our system of numeration, we use ten symbols called digits-0, 1, 2, 3, 4, 5, 6, 7, 8, and 9- and combinations of these symbols.

Variables

is mathematical representation for unknown numbers, values, or quantities.

Mathematical Expression

the mathematical analogue of a noun will be called expression

Mathematical Sentence

the mathematical analogue of sentence will also be called a sentence.

Set Theory

is the branch of mathematics that studies set of the mathematical science of the infinite.

Georg Ferdinand Ludwig Philipp Cantor

founder of set theory.

Set

is a well-defined collection of objects; the objects are called the elements or members.

E

is used to denote that an object is an element of a set.

Roster or Tabulation Method

the set are enumerated and separated by comma.

Rule Method or Set Builder Notation

it is used to describe the elements or members of a set.

Finite Set

is a set whose elements are limited or countable, and its last element can be identified.

Infinite Set

is a set whose elements are unlimited or uncountable, and the last element cannot be specified.

Unit Set

is a set with only “one” element.

Empty Set or Null Set

is a unique set with no element.

The Cardinality Number of a Set

is the number of elements or members in the given set. It is denoted by n(A).

Universal Set

is a set that contains everything.

Subset

when we define a set, if we take pieces of that set, we can form what is called a…

Union of a Set

the union of two sets A and B

Complement of a Set

if universal set (U) is having a subset then the complement of a set A which is represented as A’ contains the elements other than the elements of set A.

A’

includes the elements of the universal set but not the elements of set A.

Venn Diagrams

these are diagrams that make use of geometric shapes to show relationships between them.