# exists

Hello everyone, Everyone is looking for the perfect math that can solve all the real problems. Mathematics is a strict reasoning or one has no right to the error in this reasoning and time does not exist and many real problem are not calculable to see any sense with a classical mathematics...

Does there exists a brach of mathematics, if exists, perhaps in computational mathematics, researches the properties of multiple nesting functions where every nested function is somewhat simple, such as piecewise linear function?
3. ### Help Proving Whether a Certain Rational Exists - Tried and I'm Stumped

Trying to solve this: Let $r \in \, (0,1\, )$ and $r \notin \mathbb{Q}$. Let $râ€™ \in \, (0,1\, )$, $râ€™>r$, $râ€™ \notin \mathbb{Q}$, and $râ€™-r \notin \mathbb{Q}$. Let $q \in A = \{ râ€™-r+p : p \in \, (r,r+1\, ) \cap \mathbb{Q} \}$ Finally, one of the following statements must be true...
4. ### For every A matrix exists a B diagonal matrix that A is similar to B?

Hello I feel that this statement is not true, but I don't know how to prove it. We know that A is similar to B if there exists an invertible P matrix so that B=inv(P)*A*P Any idea how to do this?
5. ### A proposed proof that no 'perfect cuboid' exists.

'Perfect Cuboid' or 'Euler Brick' The object is to produce a 'brick' for which the dimensions of the edges, face diagonals and body (or 'space') diagonal can all be given as integers > 0, or show that no such solution is possible. The argument will show that a contradiction of parity results...
6. ### Show there exists a unique solution

y' = 1/(2y*sqrt(1-x^2)) Without solving the initial-value problem, argue that there exists a unique solution. I can solve it and all, but the existence and uniqueness kind of confuse me. I think it's along the lines of F(x,y) = 1/(2y*sqrt(1-x^2)) y=! 0, x =! +-1 Fy(x,y) = -1/(2y^2 *...
7. ### How to Know if a theorem already exists ??

Hello all, Please show me the way of knowing if a theorem already exist in math ?
8. ### Does the following composite function exists?

f: {x >5} -> R , f(x) =2^x - 70 g: (0,infinity)-> Z , g(x) = 3x + 7 The answer in the book say it doesn't exists. However , when I tried to do , I get a yes answer. Range G must be in domain of f g: = (0, infinity) Domain g = x>0 when x = 1 , g(x) = 3+7 = 10 since any positive...
9. ### Find the limit if exists

Without using L'Hospital theorm, find the limit if exists, {(-1)^n*(n+log n)}/{n+e^n}
10. ### Show that there exists a unique mapping $g:B \rightarrow A$, such that $gof=i_A$ and

please,check my answer to the folowing problem: "Let $i_A:A\rightarrow A$ and $i_B:B \rightarrow B$ be two identity mappings and let $f:A \rightarrow B$ be a bijection. Show that there exists a unique mapping $g:B \rightarrow A$, such that $gof=i_A$ and $fog=i_B$". my solution: (1) $f$...
11. ### Proving P exists in complex equation

Suppose the product of two complex numbers z1 and z2 is real and di?erent from zero. Prove that there exists a real number p such that z1 = pz2* So how do I prove it?
12. ### Proving that a limit of a function of two variables exists

Hello, I'm having problems with this type of problem: \lim_{(x,y)\to(0,0)}\frac{x^{2}y^{2}}{x^{2}+y^{2}} \lim_{(x,y)\to(0,0)}\frac{x^{2}y^{2}}{x^{2}+y^{4}} \lim_{(x,y)\to(0,0)}(x^{2}+y^{2})\sin \frac{1}{xy} I'm able to compute the limit itself, but I still need to prove that it exists. I...
13. ### When y>0 there exists a real number x such that x^2=y

This problem has stumped me. I have proven the Archimedean principle, and that there exists a rational number q such that x<q<y for all real numbers x,y where x<y (proven density), but I cannot get this one. I have also proven that if y>0 then the set of all real numbers x>0 such that x^2<y is...
14. ### Find the Limit if it exists

\lim_{x\to\(-6)}\frac{2x + 12}{|x + 6|} so i got 2(x+6)/x+6 which became 1 so i got 2*1 = 2 so the limit as x approaches (-6) = 2 correct? Or do i HAVE to use (-6) in my equation somewhere to find a limit? I wasn't sure if I could just cancel out without using it to fill some variable(s) place.
15. ### Limit exists proof

Let g_n be defined on I by g_n(x)=n(x),\ 0\le x\le 1/n g_n(x) = \frac{n}{n-1}(1-x),\ 1/n<x\le 1. Show that lim(g_n) exists on I. How can I formally prove this problem ?
16. ### Proving that a function exists

Hi everyone, I am just a high school student who is wondering if there is a simple way to prove that a function exists? For example, if I draw a random line on the plane? Thank you in advance for your efforts.
17. ### Show that there exists a matrix with certain entries and det

Hi. Here is a problem I found in my algebra book and I don't know how to solve it. Could you please help me? Here it is: Show that there exists a matrix A \in M(n,n;R), such that m_{ij} \in \{-1,0,1\} and det M=1995. My problem is that I don't know how to prove that there exist a certain matrix.
18. ### prove there exists an inverse function

I'm quite new to calculus and frankly speaking I'm studying it on my own. Could you tell me how to solve this: f: [\frac{\pi}{2}, \pi) \ni x \rightarrow \frac{1}{\sin x} \in \mathbb{R} Prove that there exists an inverese of f. In what set is f^{-1} differentiable? Calculate f^{-1'} I would...
19. ### Determining if the limit exists

Alright mine says find limit as x approaches 8+ when ((9)/(ln(x-7)-(3)/(x-8)) 1)i'm supposed to plug in 8+ into the equation, and got 0/0 2)i found common factors and got by multiplying one side by ln(x-7), and the other by (x-8) 3) I then got (9(x-8)-3ln(x-7)/(ln(x-7)(x-8) 4) once i solved that...
20. ### Simple prove why our universe and nature's laws exists.

It is easy to prove why our universe and nature's laws exists. The prove is given in 3 simple steps: Step 1 The zero vector exists. Prove At least one of both expressions (1 or 2) is true, and both lead to the same conclusion. => the conclusion is always true. Expression 1: Nothing exists (a)...