# relation

1. ### 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. ### 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. ### 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. ### 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. ### On the set N Ã— N, define the following relation: (a, b) âˆ¼ (c, d) if and only if a + d

On the set N Ã— N, define the following relation: (a, b) âˆ¼ (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. ### 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. ### 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. ### 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...

17. ### 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. ### 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. ### 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. ### 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,