Lecture

Natural Numbers

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture introduces the concept of natural numbers, focusing on the existence of numbers such as 0, 1, 2, 3, etc. The instructor explains how '2 is a natural number' and the notion of elements in the set of natural numbers. The lecture covers the properties and characteristics of natural numbers, including the empty set, subsets, and operations like addition and multiplication. It also delves into the properties of natural numbers under addition and multiplication, such as commutativity, associativity, and the existence of neutral elements.

Official source

Ontological neighbourhood

Mathematics

Mathematical logic: Set theory

Arithmetic: Topics in arithmetic

Related concepts (32)

Multiplication

Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier; both numbers can be referred to as factors.

Empty set

In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called non-empty. In some textbooks and popularizations, the empty set is referred to as the "null set".

Associative property

In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed.

Natural number

In mathematics, the natural numbers are the numbers 1, 2, 3, etc., possibly including 0 as well. Some definitions, including the standard ISO 80000-2, begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, ..., whereas others start with 1, corresponding to the positive integers 1, 2, 3, ... Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers).

Multiplication table

In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with base-ten numbers. Many educators believe it is necessary to memorize the table up to 9 × 9. The oldest known multiplication tables were used by the Babylonians about 4000 years ago.

Related lectures (64)

Understanding Equivalence Relations and Integer Construction

Covers the construction of integers through equivalence relations and their properties in mathematics.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Associative Operations: Fundamentals

Covers associative and commutative operations in parallel programming, using mathematical examples and discussing challenges in preserving associativity.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Order of Operations: Unnecessary Parentheses