Recent content by Horse

An integration of the Engines and A New Address The project has developed to the point when the integration was possible. Future goal will be to continue on the same path, making information more accessible at Mathematics. The site will be at [PLAIN]mathharbour.com[/URL] Meanwhile, you can...

Are there more books like "Abel's Theorem in Problems and Solutions"? The book "Abel's Theorem in Problems and Solutions" saved me in Algebra. I have over 5 books in Algebra, but Abel shines in its student-friendliness. It is easy to approach, full of exercises, solutions and relevant theories...

Semantic tree,... tree proof. The word is "tree proof". You can see that it is valid: http://www.umsu.de/logik/trees/?f=(\neg((\foralla\forallbPa\toPb) \rightarrow \neg (\forallb\forallcPb\toPc))))) Solved :)

The energy (=QV) is 12 \mu C * 6 V = 66 \mu J . But somethig must be wrong, as I have: Perhaps, it is 12 \mu C * 6 V = 72 \mu J . ? Dunno why ? If we suppose the logic right, we get a result for the energy emitted: 72 \mu J - 66 \mu J = 6 \mu J The amount of the thermal heat emitted...

Homework Statement A resistor, a capacitor, a battery and a switch are connected to a circuit. The capacitor will be charged from the empty state to the full state. During the period in which the capacitor is charged, how much thermal heat is emitted from the resistor? C = 2 \mu F R =...

Mathematics Search Engines I added some functions over all engines. The idea is to specialise in different engines. Then, users can navigate just by remembering some keywords: http://unmathfacts.blogspot.com/ . When they forget the urls, they can just google the unique words "Math Harbour". If...

Homework Statement Show the semantic tree of: \neg ( ( p_0 \rightarrow p_1 ) \rightarrow \neg ( p_1 \rightarrow p_2 ) ) Homework Equations \neg ( ( p_0 \rightarrow p_1 ) \rightarrow \neg ( p_1 \rightarrow p_2 ) ) The Attempt at a Solution I cannot understand its purpose...

Does the following method work? "If you can prove ( y \wedge \neg c ) \rightarrow Contradiction , then y \rightarrow c must be right."

Let's analyse them. Let p = a \vee b and y = a \wedge b. So the problems become: "If you can prove ( p \vee \neg c ) \rightarrow Contradiction , then p \rightarrow c must be right." "If you can prove ( y \vee \neg c ) \rightarrow Contradiction , then y \rightarrow c must be right."...

New Problem Prove a \vee b \rightarrow c Conjecture, according to my last proof: "If you can prove ( a \vee b \vee \neg c ) \rightarrow Contradiction , then a \vee b \rightarrow c must be right." It is similar to the last proof by contradiction: "If you can prove ( a \wedge b \vee...

Let's simplify. I know for sure:\neg ( a \rightarrow b ) = a \wedge \neg b So ( a \rightarrow b ) = \neg a \vee b If I want to prove ( a \rightarrow b ), then the finding a \wedge \neg b \rightarrow Contradiction will prove it. Please, notice that \neg ( a \rightarrow b ) \rightarrow...

Nice reply! Perhaps, something like: \lambda_{1} = \frac{\alpha \pm \sqrt{\alpha^{2}+4\beta}}{2} \lambda_{2} = \frac{\alpha \pm \sqrt{\alpha^{2}+4\beta}}{2} not sure though how it will solve the problem.

Homework Statement Prove or disprove: "If you can prove ( y \wedge \neg c ) \rightarrow Contradiction , then y \rightarrow c must be right."Homework Equations My teacher used the sign \wedge , instead of \vee , like: "If ( a \wedge b \wedge \neg c ) \rightarrow Contradiction , then...

Great thanks for the awesome tip!

I am sorry of the blurry image. I wanted to know why the relation is true: \frac{AC^2}_{CB^2} is proportional to \frac{[ACD]}_{[CDB]}