Like this blog?- New webpage at www.vadimkulikov.org March 24, 2017
- (Ir)rational Behavior of Calculation October 18, 2011
- The Product of Topological Spaces Does Not Obey Cancellation October 12, 2011
- Wild Embeddings October 11, 2011
- Progress October 4, 2011
- Class-metric August 24, 2011
- Intellectual Lazyness August 22, 2011
- Time Limit: One Minute! August 17, 2011
- Douglas Hofstadter: I Am a Strange Loop. August 15, 2011
- 0.999999……=1? (continuation) July 10, 2011
- Walks on Planets July 5, 2011
- 0.999999….. = 1? July 3, 2011
- Prisoners’ problem 6 June 29, 2011
- I am back! June 28, 2011
- A non-associative “group” March 21, 2011
- Why I haven’t blogged March 21, 2011
- Doodling with Fractals and Persistent Worms. January 2, 2011
- Five groups November 23, 2010
- Splitting A Rectangle November 17, 2010
- Sphere November 10, 2010
Category Archives: Foundations
The Most Important Relation In Mathematics 1
Part 1: Basics In this and few following posts I will argue that not only in mathematics, but in all human reasoning, the role of equivalence relations is crucial. The notion of an equivalence relation is the key to any … Continue reading
Posted in Education, Foundations, Mathematics, Philosophy
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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
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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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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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