Least-upper-bound property

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11. Thank you for the invitation. 2. I gave an invited talk at CCA in Hagen, I think it was in 2008, where I spoke about real numbers. Today I am speaking about real numbers again. You know what to expect the next time.

1. Thank you for the invitation. 2. I gave an invited talk at CCA in Hagen, I think it was in 2008, where I spoke about real numbers. Today I am speaking about real numbers again. You know what to expect the next time.

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Source URL: math.andrej.com

Language: English - Date: 2016-06-16 04:03:45
2In defence of Dedekind and Heine–Borel Paul Taylor Third Workshop on Formal Topology Padova, mercoled`ı, il 9 Maggio 2007

In defence of Dedekind and Heine–Borel Paul Taylor Third Workshop on Formal Topology Padova, mercoled`ı, il 9 Maggio 2007

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Source URL: www.paultaylor.eu

Language: English - Date: 2009-02-12 12:35:14
3The Dedekind Reals in Abstract Stone Duality Andrej Bauer and Paul Taylor 3 June 2009 Abstract Abstract Stone Duality (ASD) is a direct axiomatisation of general topology, in contrast to the traditional and all other con

The Dedekind Reals in Abstract Stone Duality Andrej Bauer and Paul Taylor 3 June 2009 Abstract Abstract Stone Duality (ASD) is a direct axiomatisation of general topology, in contrast to the traditional and all other con

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Source URL: www.paultaylor.eu

Language: English - Date: 2009-06-03 17:25:38
4Interval Analysis Without Intervals Paul Taylor 20 February 2006 Abstract We argue that Dedekind completeness and the Heine–Borel property should be seen as part of the “algebraic” structure of the real line, along

Interval Analysis Without Intervals Paul Taylor 20 February 2006 Abstract We argue that Dedekind completeness and the Heine–Borel property should be seen as part of the “algebraic” structure of the real line, along

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Source URL: www.paultaylor.eu

Language: English - Date: 2009-02-12 13:25:28
52001 Paper 1 Question 8 Discrete Mathematics Let (A, 6A ) and (B, 6B ) be partially ordered sets. (a) Define the product order on A×B and prove that it is a partial order. [4 marks]

2001 Paper 1 Question 8 Discrete Mathematics Let (A, 6A ) and (B, 6B ) be partially ordered sets. (a) Define the product order on A×B and prove that it is a partial order. [4 marks]

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Source URL: www.cl.cam.ac.uk

Language: English - Date: 2014-06-09 10:17:39
6INDUCTION AND COMPLETENESS IN ORDERED SETS PETE L. CLARK Abstract. We define an inductive subset of an ordered set and show that an ordered set X is Dedekind complete iff the only inductive subset of X is X itself. Thi

INDUCTION AND COMPLETENESS IN ORDERED SETS PETE L. CLARK Abstract. We define an inductive subset of an ordered set and show that an ordered set X is Dedekind complete iff the only inductive subset of X is X itself. Thi

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Source URL: math.uga.edu

Language: English - Date: 2013-09-10 16:37:35
7Lecture 3 Limits In the previous lecture, we used the least upper bound property of the real numbers to define the basic arithmetic operations of addition and multiplication. In effect, this involved finding sequences wh

Lecture 3 Limits In the previous lecture, we used the least upper bound property of the real numbers to define the basic arithmetic operations of addition and multiplication. In effect, this involved finding sequences wh

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Source URL: math.caltech.edu

Language: English - Date: 2013-10-14 09:59:36
8Lecture 4: Cauchy sequences, Bolzano-Weierstrass, and the Squeeze theorem The purpose of this lecture is more modest than the previous ones. It is to state certain conditions under which we are guaranteed that limits of

Lecture 4: Cauchy sequences, Bolzano-Weierstrass, and the Squeeze theorem The purpose of this lecture is more modest than the previous ones. It is to state certain conditions under which we are guaranteed that limits of

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Source URL: math.caltech.edu

Language: English - Date: 2013-08-13 12:27:41
92 Sequences and Series In this chapter we will study two related questions. Given an infinite collection X of numbers, which can be taken to be rational, real or complex, the first question is to know if there is a li

2 Sequences and Series In this chapter we will study two related questions. Given an infinite collection X of numbers, which can be taken to be rational, real or complex, the first question is to know if there is a li

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Source URL: www.math.caltech.edu

Language: English - Date: 2010-10-16 18:41:12
10Lecture 2: The real numbers The purpose of this lecture is for us to develop the real number system. This might seem like a very strange thing for us to be doing. It must seem to you that you have been studying real numb

Lecture 2: The real numbers The purpose of this lecture is for us to develop the real number system. This might seem like a very strange thing for us to be doing. It must seem to you that you have been studying real numb

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Source URL: math.caltech.edu

Language: English - Date: 2013-08-06 12:25:56