filmov
tv
Proof: Supremum and Infimum are Unique | Real Analysis
Показать описание
If a subset of the real numbers has a supremum or infimum, then they are unique! Uniqueness is a tremendously important property, so although it is almost complete trivial as far as difficulty goes in this case, we would be ill-advised to not prove these properties! In this lesson we'll be proving the uniqueness of suprema and infima.
Recall that the supremum of A, denoted sup A, is the least upper bound of A. The infimum of A, denoted inf A, is the greatest lower bound of A.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
********************************************************************
+WRATH OF MATH+
Follow Wrath of Math on...
Recall that the supremum of A, denoted sup A, is the least upper bound of A. The infimum of A, denoted inf A, is the greatest lower bound of A.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
********************************************************************
+WRATH OF MATH+
Follow Wrath of Math on...
0:04:21
Proof: Supremum and Infimum are Unique | Real Analysis
0:10:20
Proof: Supremum of {n/(n+1)} = 1 | Real Analysis
0:09:10
Real Analysis 6 | Supremum and Infimum
0:04:34
Proof: Supremum of {1/n} = 1 | Real Analysis
0:13:51
Definition of Supremum and Infimum of a Set | Real Analysis
0:11:07
Epsilon Definition of Supremum and Infimum | Real Analysis
0:03:21
2.5 Supremum: proof - sup(0,1)=1
0:16:10
Real Analysis | The Supremum and Completeness of ℝ
1:50:00
Cauchy Completeness
0:03:19
Proof: Minimum of a Set is the Infimum | Real Analysis
0:05:50
Supremum & Infimum --- Part 1 --- Supremum, Example and Completeness Axiom
0:03:23
7.4 The supremum and infimum of a function
0:07:54
How to use the epsilon definition of sup in a proof
0:36:17
Advanced Calculus I, Part 3, Completeness Axiom, Supremum, Infimum
0:07:31
Supremum, Infimum: Definition and Explanation
0:05:21
Proof: Infimum of {1/n} = 0 | Real Analysis
0:11:41
Supremum & Infimum are unique | Property | Real Analysis | glb | lub | upper/lower bound | Msc |...
0:15:46
Fundamental Properties of Supremum and Infimum, Including sup(A + B) = sup(A) + sup(B)
0:04:28
Sup(1- 1/n), n is natural number | Sup(A) and Inf(A) | Use of Archimedean Property
0:14:52
Uniqueness of supremum & Infimum....theorem to prove supremum's condition
0:05:35
Proof: Maximum of a Set is the Supremum | Real Analysis
0:26:04
Supremum and Infimum (Sup and Inf) Definitions and Examples, Prove sup{cos(n) | n in N} Equals One
0:00:50
Two step #proof for a #supremum
0:10:02
Infimum and Supremum Examples (Real Analysis)
Комментарии