big list - Conjectures that have been disproved with extremely …
Jul 23, 2010 · The first counterexample found has 96 vertices. The "least" counterexample known has 54 vertices. Heidetniemi conjecture; Chromatic number of tensor product of finite undirected simple graph is equal to the least of chromatic numbers of those graphs. The first known counterexample to this conjecture has more than $4^{10000}$ vertices. Thom ...
Ideas of finding counterexamples? - Mathematics Stack Exchange
Sometimes blindly constructing a counterexample works. In certain situations, you can look at the list of properties a counterexample needs to satisfy and just write down an example which satisfies the first property, modify it to satisfy the second, etc. and there will be essentially no obstruction to doing this.
What is an example of a proof by minimal counterexample?
Nov 17, 2018 at 19:25. 1. Any uneven natural number is prime. Counterexample 9 = 3*3. – Uwe. Nov 17, 2018 at 21:52. 3. (If I understand correctly) "proof by minimal counterexample" proves that a minimal counterexample does not exist (wikipedia), and the 2 comments above are not correct. – user202729.
Egorov's Theorem - Counterexample in Infinite Case
Why does Egorov's theorem not hold in the case of infinite measure? It turns out that, for example, fn =χ[n,n+1]x f n = χ [n, n + 1] x does not converge nearly uniformly, that is, it does not converge on E such that for a set F m (E\F) < ϵ ϵ. Is this simply true because it takes on the value 1 for each n but suddenly hits 0 when n ...
discrete mathematics - How can I provide a counterexample for …
Mar 9, 2016 · $\begingroup$ To give a counterexample you must interpret the argument formally, forgetting about lions & animals. The logical form is: All L's are A's, and all L's are M's; therefore all A's are M's. This is obviously false. For a simple counterexample, interpret L, A, and M so L is a subset of M and M is a proper subset of A.
Using proof by contradiction and a counter example.
Jul 13, 2017 · A real proof by contradiction will arrive at some kind of internal contradiction. A very good example is the proof that 2–√ 2 is irrational. You assume it is rational, then write it in lowest terms as a b a b. From a2 = 2b2 a 2 = 2 b 2, you derive that both a a and b b are divisible by 2 2, so a b a b can't be in lowest terms after all.
A counterexample in topology - Mathematics Stack Exchange
8. Call the "interesting" point in the Hawaiian earring q q (the point where all the circles intersect). In your space X X, glue the quotiented point {H × {0}} {H × {0}} to the point (q, 1) ∈ H × I (q, 1) ∈ H × I, essentially bending your cone around in a loop. Call the resulting quotient space Y Y, and the glued point p p.
Counterexample to Kunneth Formula - Mathematics Stack Exchange
Oct 7, 2021 · Counterexample to Kunneth Formula. I'm reading Example 9.14 of Bott&Tu's Differential Forms in Algebraic Topology, which gave a counter example to the Kunneth formula when the assumption is not satisfied by constructing manifolds M M and F F such that H0(M × F) H 0 (M × F) is naturally isomorphic to RZ×Z R Z × Z while H0(M) ⊗H0(F) H 0 (M ...
Advice on finding counterexamples - Mathematics Stack Exchange
1,364 2 14 28. 5. To find counter-examples, you must at least be able to write down examples. Here are some groups you should know: Sn S n, D2n D 2 n, Z/nZ Z / n Z. Now play! – RghtHndSd. Mar 31, 2015 at 19:31. 3. @valentino This is a very valuable skill, and maybe not the easiest to acquire.
Convergence types in probability theory : Counterexamples
Then P(| Xn |> ϵ) = 1 n → 0 asn → ∞ for any ϵ ∈ (0, 1). This shows that Xn → 0 in probability. Since EXn = n ⋅ 1 n = 1 the sequence does not converge to 0 in L1. Note that L1 -convergence fails although the random variables are integrable. (Just as a side remark: This example shows that convergence in probability does also not ...