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- New webpage at www.vadimkulikov.org March 24, 2017
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# Monthly Archives: January 2010

## The Coin Placing Game.

See the Wednesday Problem’s vague rules here. Some games again. According to Sam, from whom I heard this riddle, it divides people into cathegories i) those who realize the answer immidiately and ii) those who think quite long about it. … Continue reading

Posted in Games, Recreation, Wednesday Problem
6 Comments

## TopoLogic

The Continuum Hypothesis trilogy will continue later. Today I’ll recall some discussion I made a year ago or so in the student seminar. I guess someone would say that it is surprising, how closely related these two branches of mathematics … Continue reading

Posted in Logic, Mathematics, Topology
2 Comments

## How Old Are The Kids?

Please comment your solutions, questions and remarks.. This is quite famous. But maybe you haven’t heard it yet: A math student goes to a party organized by her supervisor. The student asks: How many daughters do you have? And the … Continue reading

Posted in Combinatorics, Recreation, Wednesday Problem
2 Comments

## 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

## The Monk

Please comment your solutions, questions and remarks.. The posts have been a bit advanced lately. Let us lighten the atmosphere by this riddle which admits a simple solution, though mathematicians tend to use calculus in solving it: An Indian monk … Continue reading

Posted in Calculus, Recreation, Wednesday Problem
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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