Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [examples-counterexamples]

To be used for questions whose central topic is a request for examples where a mathematical property holds, or counterexamples where it does not hold. This tag should be used in conjunction with another tag to clearly specify the subject.

Examples and counterexamples are great ways to learn about the intricacies of definitions in mathematics. Counterexamples are especially useful in topology and analysis where most things are fairly intuitive, but every now and then one may run into borderline cases where the naive intuition may disagree with the actual situation that follows from the definitions. This tag should be used in conjunction with another tag to clearly specify the subject.

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Is counterexample a proof?

For example, I have to proof statement: if random variables $X$ and $Y$ are merely marginally normally distributed and uncorellated it is not enough to deduce the normality of the vector $(X,Y)$ I found a counterexample, that will show the truth of…
Daniil Yefimov
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Example for associative, commutative operations

I need examples of binary operations for real numbers that are associative and commutative associative but not commutative The examples are for a programming class and need to be rather simple. Thus the operations have to work on real numbers and…
Make42
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example verification partial order

Let A= { 1, 2, 3} then R= { (1, 1), (2, 2) , (3, 3) , (1, 2), (2, 3) } ,the relation R is reflexive and anti-symmetric,i get it, but how is it following the transitive property for it to become partial order relation of set A?,really need to…
Sain Kale
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Proof by counter-example

As is probably obvious by the title I cannot work out any set of numbers which disporoves the following conjecture $$ a^2 > b^2 => a > b $$ where A and B are real numbers. Anyone to give a push in the right direction as I'm reaching the point of…
Abby
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About Linear Combination and proof

i have a question about proofing but i dont understand exactly, the question asked me whether the following expression is true or not, if it is true i need to prove that but if it is false, give counterexample is enough, The expression : "If a…
whenever07
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