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
Monthly Archives: March 2010
How Many Good Colorings?
Please comment your solutions, questions and remarks.. Suppose G is a graph in which each vertex has three neighbours, for example: Suppose we have three colors, red green and blue, with which we want to color the edges of the … Continue reading
Posted in Algebra, Combinatorics, Mathematics, Wednesday Problem
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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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Andre’s Reflection Method
I promised to post something about random walks. I learned the content of this post while listening to Vilppu Tarvainen’s bachelor’s degree talk and I consider it is quite cute. Let us consider a one dimensional random walk: formally it … Continue reading
Posted in Combinatorics, Mathematics, Probability, Recreation
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Back To College
Please comment your solutions, questions and remarks.. Show that the following inequality holds for all [tex]k>0[/tex] and [tex]x\in \mathbb{R}[/tex]: [tex]e^x>kx-k\ln k.[/tex] Level 1/5
Posted in Calculus, Mathematics, Wednesday Problem
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Even More On BFPT
I wouldn’t mind writing this unless I haven’t already posted two different proofs of Brouwer’s Fixed Point Theorem. Namely a friend of mine and a reader of this blog, exposed me to another way of proving it. This proof has … Continue reading
How Many Are True?
Please comment your solutions, questions and remarks.. At most 1 statement of this post is true. At most 2 statements of this post are true. At most 3 statements of this post are true. At most 4 statements of this … Continue reading
Posted in Logic, Mathematics, Recreation, Wednesday Problem
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Solution To The Previous Problem
Exceptionally I will present a solution to the previous Wednesday Problem. Only not shall I present any simplest solution but a cool one. The question was the following. Suppose a function [tex]f\colon \mathbb{R}\to\mathbb{R}[/tex] has the property that given any reals … Continue reading
Posted in Calculus, Mathematics
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Intermediate Value Functions
Please comment your solutions, questions and remarks.. A continuous function [tex]f\colon\mathbb{R}\to\mathbb{R}[/tex] on the real numbers has the following property: Given any two reals a<b, the function f gets all possible values between f(a) and f(b) on the interval [a,b] (i.e. … Continue reading
Posted in Calculus, Mathematics, Wednesday Problem
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