proof writing - Proving statements vs disproving statements . . . I searched online for other ways to disprove statements that didn't require a counterexample I came across this pdf: "How to disprove statements" In this they introduce the concept of disproof: It turns out that there is a very simple and utterly convincing procedure that proves a statement is false
What is the correct way of disproving a mathematical statement? Assuming the thing you want to disprove and inferring something you know to be false This is called reductio ad absurdum, or proof by contradiction It may seem bizarre to assume a (possibly) false proposition, but what you are really doing is considering the truth value of propositions conditional on the proposition you want to disprove
computer science - Disproving big O - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Disprove: If $f$ is Riemann integrable on $ [a, b]$, then $f$ is . . . Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Prove or disprove: $(A-B)-C=(A-C)- B$ for sets $A$, $B$, $C$ Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
How to Disprove $A-(B-C)=A-(B\\cup C)$? For $A,B,C$ sets. Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
inequality - (Dis)proving $\cos (A+B) \leq \cos B +\cos A$ in . . . $$\cos (A+B)\leq\cos A +\cos B$$ $$\iff\cos (\pi-C)\leq\cos A +\cos B$$ $$\iff-\cos C\leq\cos A +\cos B$$ $$\iff0\leq\cos A +\cos B+\cos C$$ $$\iff0\leq 1+4\sin\frac A2\sin\frac B2\sin\frac C2$$ due to the formula $$\cos A+\cos B+\cos C=1+4\sin\frac A2\sin\frac B2\sin\frac C2$$ in a triangle $\triangle ABC $ Now, each half angle is less than $90^\circ$ so in fact $$1< 1+4\sin\frac A2\sin\frac
Prove or disprove that the sum of two irrational numbers is irrational . . . When a statement like that is given to prove or disprove, " sum of two irrationals is irrational" , it is proved if it is found to be always true and disproved if at least one counter example can be given In fact, sum of two irrationals can be either rational or irrational
Disprove: If a graph - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers