Integers: Well Ordering and Induction

In course

Description

This lecture covers the principles of well ordering and induction, including the Euclidean division, Bezout's theorem, and the Euler totient function. It explains the concepts step by step, demonstrating how to apply them in various examples and scenarios. The lecture also delves into the uniqueness of prime factorization and the properties of integer arithmetic, providing a solid foundation for understanding number theory.

Instructor

Official source

https://mediaspace.epfl.ch/media/0_6gzrp8nw

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related lectures (510)

Related concepts (193)

IPhone

iPhone is a line of smartphones produced by Apple Inc. that use Apple's own iOS mobile operating system. The first-generation iPhone was announced by then-Apple CEO Steve Jobs on January 9, 2007. Since then, Apple has annually released new iPhone models and iOS updates. As of November 1, 2018, more than 2.2 billion iPhones had been sold. As of 2022, the iPhone accounts for 15.6% of global smartphone market share. The iPhone was the first mobile phone to use multi-touch technology.

IPhone X

The iPhone X (Roman numeral "X" pronounced "ten") is a smartphone designed, developed and marketed by Apple Inc. It is part of the eleventh generation of the iPhone. Available for pre-order from October 27, 2017, it was released on November 3, 2017. The naming of the iPhone X (skipping the iPhone 9) is to mark the 10th anniversary of the iPhone. The iPhone X used a glass and stainless-steel form factor and "bezel-less" design, shrinking the bezels while not having a "chin", unlike many Android phones.

IPhone 14

The iPhone 14 and iPhone 14 Plus are smartphones designed, developed, and marketed by Apple Inc. They are the sixteenth and latest generation of iPhones, succeeding the iPhone 13 and iPhone 13 Mini, and were announced during Apple Event, Apple Park in Cupertino, California, on September 7, 2022, alongside the higher-priced iPhone 14 Pro and iPhone 14 Pro Max flagships. The iPhone 14 and iPhone 14 Plus feature a and display, improvements to the rear-facing camera, and satellite connectivity for contacting emergency services when a user in trouble is beyond the range of Wi-Fi or cellular networks.

IPhone 4s

The iPhone 4s is a smartphone that was designed and marketed by Apple Inc. It is the fifth generation of the iPhone, succeeding the iPhone 4 and preceding the iPhone 5. It was announced on October 4, 2011, at Apple's Cupertino campus, and was the final Apple product announced in the lifetime of former Apple CEO and co-founder Steve Jobs, who died the following day. Orders could be placed on October 7, 2011, and mainstream availability in retail stores began on October 14, 2011 in the United States, Australia, Canada, the United Kingdom, France, Germany, and Japan.

History of the iPhone

The history of the iPhone development by Apple Inc. spans from the early 2000s to about 2010. The first iPhone was released in 2007. By the end of 2009, iPhone models had been released in all major markets. The idea of an Apple phone came from Jean-Marie Hullot, a software engineer from NextStep, and later, MacOS. Initially, making an Apple phone was not favored by CEO Steve Jobs, but eventually Hullot was able to convince him.