1. idontknow

    Need help to verify the number of solutions

    Given equation x^2 +x +\lambda =0 \; ,x\in \mathbb{R}. Verify N - the number of solutions, using any software (matlab, calculators... etc.) N_{\lambda } =\frac{\displaystyle 1 + \lim_{s\rightarrow \infty} \left[-2\left(1+e^{-2s(-1-4\lambda)}\right)+1\right]}{2}\lim_{s\rightarrow \infty}...
  2. P

    functions, relations, injective,...

    Hello there, I'm new to the kind of math you have to prove, so be patient ^^ Are there any improvements I could make here? In the following, I will talk about $Z$ as a ring. More specifically I consider $(Z,+,\times)$ a commutative and unitary ring, where $Z = \{...,-2,-1,0,1,2,...\}$. I...
  3. HazyGeoGeek

    Non-Linear Relation

    Could someone tell me about the relation in the attached image. One in the top follows the linear relation and extended length can be obtained through multiplying the height*angle. What would be relation for bottom one?
  4. S

    Transitive Relation

    Hello, Should the variables (x and y and z) in transitive relation be different numbers? or x,y, and z can be equal? For example we have: R = { {1,1}, {1,2} , {1,3} } Is R transitive? because we have: {1,1} {1,1} => {1,1} {1,1} {1,2} => {1,2} {1,1} {1,3} => {1,3} Thanks
  5. E

    On the set N × N, define the following relation: (a, b) ∼ (c, d) if and only if a + d

    On the set N × N, define the following relation: (a, b) ∼ (c, d) if and only if a + d = b + c. (1) Show that this is an equivalence relation (2) Describe the equivalence class of (1, 1)
  6. B

    What is the relation between 0^0 and limx^x?

    Since we can not divide with zero, the equation below is true for every x except zero. 1 = \frac{x^1}{x^1} = x^{1-1} = x^0 Using limits we can see that 0^0 is actually getting close to 1. lim_{x \to 0} x^x = 1 Does this say anything?
  7. J

    Recurrence relation

    For second order linear homogeneous recurrence relation with constant coefficients, is it that the general sequence is only in the form of 1, t, t^2, t^3, ..., t^n or just one of the general sequences which satisfies the characteristic equation? Thank you.
  8. P

    Eigenvectors and Eigenvalues in relation to a double transformation

    Hi guys, I have the following question: I have been thinking about this for a while now, but I simply cannot work it out... Let V be a linear space of n dimensions over R, and let S,T:V->V be linear transformations. True or False? 1. If v is an eigenvector of S and of T, then v is...
  9. 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...
  10. P

    Matrix in relation to solution subspace

    Hi guys, I am having serious trouble analysing the following question: I have been thinking about it for an hour, but I am not progressing… Can anybody help out? Let A be a matrix over R of order 4x4, with rank 2. Suppose that the vectors u=(2,1,2,0) v=(1,-1,2,4) w=(1,0,2,-1) are...
  11. S

    Q: Let S = {x, y, z } and R be a relation defined on S such that

    Q: Let S = {x, y, z } and R be a relation defined on S such that R = {(y,y),(x,z),(z,x),(x,x),(z,z),(x,y),(y,x)} Show that R is reflexive and symmetric as well.
  12. S

    Q: Let S = {1,2,5,6} Define a relation R on S of at least four order pairs

    Q: Let S = {1,2,5,6} Define a relation R on S of at least four order pairs, as (a,b) ∈ R iff a*b is even (i.e. a multiplied by b is even).
  13. M

    Find the relation

    The problem is My Attempt: 2r\pi + 4x = 2, d/dx(r^2\pi + 4x^2) = 0; But both the equations does not seem to give me the result. Please help.
  14. C

    relation between order of polynomial fit and range of x data

    Hi everybody, I have y-data that span an x-data range of say 1:100. The data are nicely fitted with a polynomial fit of 3rd order (Matlab/python: polyfit(x,y,3)). I have a second set of y-data (say: yy), spanning only half of the data range, say x=51:100. Is there any reasonable...
  15. L

    Equivalence Relation

    I have come across a question as "The number of equivalence relations that can be defined on a set with two elements is " and same question for 3 elements as well. Since I have the answers with me I am thinking the possible general term would be 2^n - n Someone correct me😊
  16. T

    Legendre reccurence relation

    I am having a slight issue with generating function of Legendre polynomials and shifting the sum of the generating function. So here is an example: I need to derive the recurrence relation $lP_l(x)=(2l-1)xP_{l-1}(x)-(l-1)P_{l-2}$ so I start with the following equation...
  17. M

    Injective relation

    Hello, I'm trying to work on the following: Let A be a subset of a set E. F is the relation that associates each X of P(E) with the symmetric difference of A and X. Show that F is injective. My idea has been to use the definition of an injective relation to show that for X and X' in P(E)...
  18. H

    Find the relation between (a) and (b)

    Hi everyone, If the line y = ax+b is tangential to the unit circle, then find the relation between (a) and (b). Any help please?
  19. M

    several questions about relations and functions

    Hello, I'm having trouble with the concept of relations and functions. I don't understand some concepts and I'd like your help to do that if you can. Let's say we have a simple set M that is the relation set of A={1,2,3}. a) the number of elements of M? Is it 1M3,1M2,2M1,2M3,3M1,3M2,3M1 or do...
  20. siri

    How to find order of a recurrence relation? help

    Hi, I'm in a hurry, for example : an= an-1 + an^2-2 there order of this function is "2" how is that be? and what is the meaning of order please help me,