1. J

    Relation Algebra, why is this PDL sentence equivalent

    In the book modal logic for open minds by johan van benthem there is on page 161 a statement that the sentence $\langle (R\lor S)* \rangle \phi$ is equivalent to the sentence $\langle (R* ; S*)* \rangle \phi$ (* means iteration and ; means composition here) So: $\langle (R\lor S)* \rangle...
  2. J

    Equivalent fraction of "ONE"

    Hello guys, what is up? Well, today I'm going to talk about FRACTIONS. There's a curious property in fractions and as simple as it seems however I couldn't figure it out. I'm still trying get the idea. Such property's going to be illustrated down: First we have a general property that...
  3. I

    Equivalent Expressions (Trig)

    Help!!!!!!!!!!!!!!!!!!!!!!!! What is the equivalent expression of: cos (pi/2 + x)/cos (pi + x)
  4. N

    Asymptotically equivalent series

    \sum_{n=1}^{\infty}n^2 \sin \frac{x}{n^4} Is it possible, in order to find intervals of uniform convergence, to study the asymptotically equivalent series \sum_{n=1}^{\infty}n^2 \frac{x}{n^4} thanks to power series theorem? Thanks a lot!
  5. V

    Need some help with equivalent matrices

    I can't seem to understand how to solve this. I'm given two 2x2 matrices: A= 1-x x 2 1+x and B= 1 1 0 1 I'm asked to find the value of x in order for A and B to be equivalent. Can anyone help? Also, I'm sorry I didn't use latex but I have totally forgot how...
  6. mahlbeck22

    Showing a multivalued function's range is equivalent to N?

    Here is a problem I have been looking at in relation to the Collatz Conjecture, I am stuck and need some direction. There is a bit of setup needed. Let $C$ be a function such that $C : \mathbb{N} \mapsto M$ where $M \subset N$ such that $M = \{\{a , b\} : a \in \mathbb{N} \text{ and } b \in...
  7. Z

    Row Equivalent 3x3 Matrices

    Are these matrices row equivalent? \begin{vmatrix} x^{3}+ax^{4}+3c & 1 & a^{2}(bc)\\ \ln(abc)+5x& 1 &bsin^{3}x+a+c \\ ax^{5}+xa^{b}+cx^{3} & 1 & 10+\frac{x^{2}}{\arctan{ac} +x} \end{vmatrix}\equiv \begin{vmatrix} a & 1 &a+b \\ b& 1 &2c \\ c & 1 & a \end{vmatrix}
  8. F

    How can these expressions be equivalent?!

    32x^4+16x^3= 2x+1 32x^4+48x^3=​2x+3 ​​ ​ ​
  9. M

    Unit Disk Equivalent to Entire Space

    Define $D^n = \{ x \in R^n: \vert x \vert < 1 \}$. Several authors, e.g. Lee, Bishop and Goldberg, identify a homeomorphism $f: D^n \rightarrow R^n$ as $f(x) = \frac{x}{1-\vert x \vert^2}$. The inverse can be computed as $f^{-1}(x) = \frac{2x}{1+\sqrt{1+4|x|^2}}$. Any thoughts on why the map...
  10. A

    Fractions & smart pirates - Fun Educational Math Game for kids

    Virtual Space is proud to announce the release of Fractions & Smart Pirates 1.3 for iOS and Android devices, offering a fun and easy way to learn fractions with the Caribbean Pirates. Recognizing and Comparing Fractions, Equivalent fractions, adding fractions - If you're struggling with fraction...
  11. J


    Are these three equivalent? -\sqrt[3]{-3}\sqrt[3]{e^{x^2+1}} \sqrt[3]{3}\sqrt[3]{e^{x^2+1}} (-1)\frac{2}{3}\sqrt[3]{3}\sqrt[3]{e^{x^2+1}}
  12. J

    Is it equivalent?

    This example is extracted from my book. \int \tan ^5xdx=\frac{1}{4}\tan ^4x-\frac{1}{2}\tan ^2x+\ln \left | \sec x \right |+c But I think it should not be \ln \left | \sec x \right |. It should be -\ln \left | \cos x \right |.
  13. J


    \int \frac{x^2-2}{x^2-1}dx My answer is x-\frac{1}{2}\ln \left | x-1 \right |+\frac{1}{2}\ln \left | x+1 \right |+c But the given answer is x-\frac{1}{2}\ln\left | \frac{x+1}{x-1} \right |+c I wonder is it equivalent or I did some mistakes ?
  14. E

    Explanation for equivalent equations

    (m+1)! - 1 + (m+1)*(m+1)! = (m+2)! - 1 Can someone tell me how the steps to do this? I'm confused at the moment. Thanks.
  15. R

    Is this equivalent to (the negation of) the Riemann hypothesis?

    Greeting ! I would be like some one to verifie me this claim if it's true : let $\zeta(s)=k(s)=\zeta(1-s) $ , it's a verified functional equation for all complex $s$ except $s=1$ . The claim is : $(\zeta o k)(s)=(ko\zeta)(s)=0 $ implies that $\zeta(s)=k(s)=0$ is true if and only if The...
  16. G

    equivalent to one millimeter of mercury?

    1)atm 2)STP 3)torr 4)14.7lb/in2 Now whats weird is the conversion factor from atm to torr(or millimeters of mercury)...so is it atm?
  17. G

    What unit is equivalent to Avogadro's number?

    1)mole 2)formula unit 3)atomic mass unit 4)none of the above I think its the mole...
  18. R

    Is the completeness of the real number line equivalent to Dedekind's axiom?

    Dedekind's axiom of continuity states that if the points of a line be divided into two classes such that every point in the first class is to the left of every point in the second class, then there exists one and only one point $P$ such that every point in the first class is to the left of $P$...
  19. R

    Is there a statement equivalent to its own converse?

    I know of a lot of pairs or sets of mathematical statements that are equivalent to each other, e.g.: Pasch's axiom and the plane separation axiom, the different statements of the axiom of choice, Playfair's axiom and Euclid's fifth postulate. That got me wondering, is there any mathematical...
  20. Monox D. I-Fly

    Is Implication Always Equivalent to Contrapositive?

    Hey everyone, I get a problem with mathematical logic. People say that implication (p \rightarrow q) is always equal to contapositive (-q \rightarrow -p). However, I encountered some examples which looked contradicting that theory. If it rains to day, Mom brings an umbrella. (p \rightarrow q)...