Order theory | Functional analysis | Mathematical analysis
In mathematical analysis and related areas of mathematics, a set is called bounded if it is, in a certain sense, of finite measure. Conversely, a set which is not bounded is called unbounded. The word 'bounded' makes no sense in a general topological space without a corresponding metric. (Wikipedia).
Every Compact Set in n space is Bounded
Every Compact Set in n space is Bounded If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Advanced Calculus
What are Bounded Sequences? | Real Analysis
What are bounded sequences? We go over the definition of bounded sequence in today's real analysis video lesson. We'll see examples of sequences that are bounded, and some that are bounded above or bounded below, but not both. We say a sequence is bounded if the set of values it takes on
From playlist Real Analysis
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
Convergent sequences are bounded
Convergent Sequences are Bounded In this video, I show that if a sequence is convergent, then it must be bounded, that is some part of it doesn't go to infinity. This is an important result that is used over and over again in analysis. Enjoy! Other examples of limits can be seen in the
From playlist Sequences
Math 101 Fall 2017 112917 Introduction to Compact Sets
Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi
From playlist Course 6: Introduction to Analysis (Fall 2017)
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Prove the Set of all Bounded Functions is a Subspace of a Vector Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Prove the Set of all Bounded Functions is a Subspace of a Vector Space
From playlist Proofs
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
This video defines finite and infinite sets. http://mathispower4u.com
From playlist Sets
Math 101 Introduction to Analysis 091815: Least Upper Bound Axiom
The least upper bound axiom. Maximum and minimum of a set of real numbers. Upper bound; lower bound; bounded set. Least upper bound; greatest lower bound.
From playlist Course 6: Introduction to Analysis
Real Analysis Chapter 1: The Axiom of Completeness
Welcome to the next part of my series on Real Analysis! Today we're covering the Axiom of Completeness, which is what opens the door for us to explore the wonderful world of the real number line, as it distinguishes the set of real numbers from that of the rational numbers. It allows us
From playlist Real Analysis
Definition of Supremum and Infimum of a Set | Real Analysis
What are suprema and infima of a set? This is an important concept in real analysis, we'll be defining both terms today with supremum examples and infimum examples to help make it clear! In short, a supremum of a set is a least upper bound. An infimum is a greatest lower bound. It is easil
From playlist Real Analysis
Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property
MIT 18.100A Real Analysis, Fall 2020 Instructor: Dr. Casey Rodriguez View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw Finishing the lecture on Cantor’s notion of
From playlist MIT 18.100A Real Analysis, Fall 2020
Math 131 090516 Lecture #02 LUB property, Ordered Fields
Least Upper Bound Property and Greatest Lower Bound Property; Fields; Properties of Fields; Ordered Fields and properties; description of the real numbers (ordered field with LUB property containing rational numbers as subfield); Archimedean property #fields #orderedfields #leastupperboun
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Epsilon Definition of Supremum and Infimum | Real Analysis
We prove an equivalent epsilon definition for the supremum and infimum of a set. Recall the supremum of a set, if it exists, is the least upper bound. So, if we subtract any amount from the supremum, we can no longer have an upper bound. The infimum of a set, if it exists, if the greatest
From playlist Real Analysis
Math 101 091317 Introduction to Analysis 06 Introduction to the Least Upper Bound Axiom
Definition of the maximum (minimum) of a set. Existence of maximum and minimum for finite sets. Definitions: upper bound of a set; bounded above; lower bound; bounded below; bounded. Supremum (least upper bound); infimum (greatest lower bound). Statement of Least Upper Bound Axiom (com
From playlist Course 6: Introduction to Analysis (Fall 2017)
Fundamentals of Mathematics - Lecture 20: Infinite Intersections and Least Upper Bound Property
course page: https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html worksheets - DZB, Emory videography - Eric Melton, UVM
From playlist Fundamentals of Mathematics
Determine Sets Given Using Set Notation (Ex 2)
This video provides examples to describing a set given the set notation of a set.
From playlist Sets (Discrete Math)
