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- New webpage at www.vadimkulikov.org March 24, 2017
- (Ir)rational Behavior of Calculation October 18, 2011
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# Category Archives: Set Theory

## Class-metric

In two weeks I start lecturing Topology I at our University. I am excited. This course was my favourite among the basic undergraduate courses. The course concentrates on metric topology and its goal is to prove simple results about complete … Continue reading

Posted in Combinatorics, Logic, Mathematics, Ramsey Theory, Set Theory, Topology, Wednesday Problem
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## Uncountable Borel Sets

Here I promised post some tough stuff. Well, I meant some fruits of our recent research by Hyttinen, Friedman and I. I will not go into the subject here, just post a link to the forthcoming paper. There is an … Continue reading

Posted in Logic, Mathematics, Set Theory
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## Prisoner’s problem 3

Please comment your solutions, questions and remarks.. There are infinitely many prisoners in a prison. The prisoners are taken to the yard and everyone is given a hat which is either black or white. No one knows the colour of … Continue reading

Posted in Combinatorics, Mathematics, Recreation, Set Theory, Wednesday Problem
Tagged Prisoners' problems
2 Comments

## Nasty Finite Combinatorics

Please comment your solutions, questions and remarks.. I was blamed for having too easy Wednesday problems. So beware! The level is coming up! Suppose that K is a set of n elements, [tex]n\in\mathbb{N}[/tex]. Suppose that [tex]K_1,\dots,K_n,K_{n+1}[/tex] are subsets of K. … Continue reading

Posted in Combinatorics, Mathematics, Set Theory, Wednesday Problem
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## Continuum Hypothesis III

Suppose you pick randomly a real number. What is the probability that it equals to 1? The probability is zero. Suppose [tex]X\subset [0,1][/tex] is a countable subset of the unit interval. What is the probability that a randomly picked real … Continue reading

Posted in Foundations, Mathematics, Philosophy, Probability, Set Theory
Tagged Continuum Hypothesis Trilogy
2 Comments

## Continuum Hypothesis II

Differentiability of Space Filling Curves A Peano curve is a surjective (onto) function [tex]f\colon\mathbb{R}\to\mathbb{R}^2[/tex]. Apparently such an f cannot be smooth. To see this consider the restrictions of this function to closed intervals [tex]f\restriction [n,n+1][/tex]. By smoothness and compactness the … Continue reading

Posted in Calculus, Foundations, Mathematics, Set Theory
Tagged Continuum Hypothesis Trilogy
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## MAD families

Please comment your solutions, questions and remarks.. Maximal Almost Disjoint families. This is not so much of a riddle than just a theorem, but the solution is fun, so I would like to place it here. This is like a … Continue reading

Posted in Combinatorics, Mathematics, Set Theory, Wednesday Problem
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## Continuum Hypothesis I

This is the first part of the forthcoming trilogy in four parts. The trilogy will be devoted to the understanding of the Continuum Hypothesis by looking at some statements that are equivalent to it. In this post I just expose … Continue reading

Posted in Foundations, Mathematics, Philosophy, Set Theory
Tagged Continuum Hypothesis Trilogy
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