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)...