Consider the following dialogue: Walter: There’s a counterexample to every generalization!Ram: Either what you just said is true or it’s false. If it’s true, then there is acounterexample to every generalization, including that very generalizationitself—and so it’s false. In this ...
What kind of equation is -2(x + 4) + 1 = -2x - 7? Which is not a counterexample to the formula 1^2 + 3^2 + 5^2 + + (2n - 1)^2 = n(2n + 1)/3? (a) n = 3 (b) n = 2 (c) n = 1 (d) n = 4 Under what situation would one or more solutions of a ration...
What is compact collection math? How many ways are there to choose 3 distinct numbers between 1 to 300 such that the sum of these 3 numbers is divisible by 3? What are some integers that are not whole numbers? What is a counterexample for the conjecture the product of two positive number...
It is also necessary to work with restricted sums rather than full sums : a counterexample to the latter is provided for instance by the example with and . Finally, the presence of the shift is also necessary, as can be seen by considering the example of being the odd numbers in , ...
For example, it is already a non-trivial result of Erdős that the series is irrational, while the irrationality of (equivalent to Erdős problem #69) remains open, although very recently Pratt established this conditionally on the Hardy–Littlewood prime tuples conjecture. Finally, the ...
In this paper we show that if a counterexample exists, then the smallest one lies in the range c3+1 D Kozen,S Zaks - 《Theoretical Computer Science》 被引量: 47发表: 1994年 Optimal Bounds for the Change-Making Problem The change-making problem is the problem of representing a given val...
Now there's nothing wrong with mastering skills, with wanting to do your best and to be the best. What's wrong is what the system leaves out: which is to say, everything else. I don't mean that by choosing to excel in math, say, you are failing to develop your verbal abilities ...
Hi all, I'm having a discussion with a friend. I hope this is the right forum. My friend's first issue: He believes in science, but does not believe in...
If this is a T-F question, the answer is false. It is true that if a number is divisible by 6, it also divisible by 3. This is true because 6 is divisible by 3. However, the converse -- If a number is divisible by 3, it is divisible by 6, is false. A counterexample is 15...
Posted by Dirk under Math, Teaching, Uncategorized | Tags: eigenvalues, eigenvectors, Jordan canonical form, linear algebra | [5] Comments I remember from my introductory class in linear algebra that my instructor said It is impossible to calculate the Jordan canonical form of a matrix numerica...