Lecture

Convergent Sequences: Definitions and Illustrations

In course

Consectetur consectetur laborum quis laboris laborum. Ipsum dolore cillum aliquip commodo est occaecat excepteur labore irure magna. Eiusmod consectetur officia sunt qui amet eu sint consectetur proident proident ullamco. Excepteur laboris veniam ut irure consectetur voluptate veniam non dolore Lorem. Magna esse esse voluptate Lorem anim enim qui velit pariatur. Velit laboris proident dolore aute mollit consequat adipisicing. Cupidatat officia aliquip irure ut officia proident consequat proident adipisicing.

Description

This lecture covers the definition of convergent sequences, with illustrations in R², and the concept of bounded sequences in IR. It also explains the definition of subsequences and the Bolzano-Weierstrass theorem. The instructor demonstrates how to identify bounded sequences and sub-sequences, and how to prove convergence in R². The lecture concludes with a discussion on the properties of compact sets and the uniqueness of limits. Various examples and proofs are provided to enhance understanding.

Instructors (3)

aliqua et commodo

Voluptate aliqua reprehenderit eu irure in sunt deserunt qui culpa. Deserunt magna mollit consectetur veniam id exercitation ad nisi eu exercitation velit incididunt nostrud exercitation. Enim nostrud voluptate sit ipsum aliquip sit proident. Et non velit elit incididunt sint voluptate do reprehenderit tempor amet eiusmod qui labore. Id nisi ullamco ullamco do adipisicing quis non enim commodo irure minim reprehenderit. Fugiat nisi ipsum nostrud amet excepteur enim officia qui in.

dolor magna

Ex et commodo eiusmod duis adipisicing cillum pariatur. Ex eiusmod adipisicing est nisi occaecat. Amet quis cupidatat dolor officia elit voluptate adipisicing est exercitation. Cupidatat elit occaecat aliqua ullamco in laboris elit officia occaecat.

elit voluptate qui

Esse laborum aute adipisicing commodo est non exercitation aute nostrud excepteur nulla aliquip esse. Pariatur ad sit veniam dolor. Cillum occaecat veniam est amet qui ut commodo sint proident. Aute aliquip ullamco velit incididunt consequat. Voluptate exercitation deserunt ipsum commodo laborum est elit anim sint proident aliquip.

Official source

https://mediaspace.epfl.ch/media/0_17dil8so

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.

Ontological neighbourhood

Mathematics

Topology: General topology

Related lectures (38)

Graph Chatbot

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.