Homework Statement
Prove that set of all onto mappings of A->A is closed under composition of mappings:
Homework Equations
Definition of onto and closure on sets.
The Attempt at a Solution
Say, ##f## and ##g## are onto mappings from A to A.
Now, say I have a set S(A) = {all onto mappings of A...
The question says that A= R-{0} and B =R. Then, that f:A ->B and I need to show whether they 1-1 and whether they are onto. Prove.
Thanks for the hint.
Homework Statement
I need to show that $$\frac{x}{x^2+1}$$ is either onto or not.
My domain is $$R-{0}$$ and range is $$R$$
Homework Equations
I have learn to do this to show that a function is surjective
y = $$\frac{x}{x^2+1}$$ and solve for x, but I am not sure how to proceed here.
The...
Homework Statement
I have found the roots of my polynomial:
## (2x+3y)^{2}-1 =0 ##
Roots are x=3n+2 & y=-2n-1, where n belongs to all Z.
What does it mean that the solution has arbitrary large coordinates?
The Attempt at a Solution
I think I know the basic concept of root. It could be...
So, here is the solution.
## \dfrac{ |n| !}{ |n_{1}|! |n_{2}|!... |n_{k}|!} \text{, where n is the size of the vector and the values in denominator are types of symbols in n that repeat.}## ##\text{For instance, if I have a vector called v={e, i, g, e, n, v, a, l, u, e}, there are say n1 type...
Please, check the solution in attachment.
Apparently, it is incorrect. Can someone verify?
I think that I am not taking into account cases such as {m, o ,m } or {1,0,1}, where there could be repetitions.
The solution should be in the form:
Order matters
{ ... , <at least digits from 0 to...
It turns out that order does matter after all. One 'gotta' love language.
An example helped to elucidate.
Example:
{0,1,2,3,...,8,9, ...<whatever>,...} is a vector of size n and 1 solution that satisfies the constraints.
{3,4,7,...,9,2,1,...<whatever>,... } is another vector of size n and...
The question is for a Theoretical Computer Science class.
You might be right, but he said that it does not matter. My professor was very vague in posing the question. I asked it twice.
He gave some examples:
## {0, 0, 0,0, ...,0_{n} }={0} ##
## {0, 0, 0, ..., 0, 1_{n}}={0,1}##
Yes, it is...
Homework Statement
Compute how many n-digit numbers can be made from the digits of at least one of {0,1,2,3,4,5,6,7,8,9 }
Assume, repetition or order do not matter.
Homework Equations
## a_{1}, a_{2}, ..., a_{n} ##
The Attempt at a Solution
10 choices for the 1st sub-index, 10 choices for...
Homework Statement
-arctan(x/y) = arctan(y/x) ?
Are they equivalent? I can't find anything online and I have seen that my solution to some problem involves
-arctan(x/y) and it agrees with Wolfram Alpha. On the other hand, my professor's solution shows the arctan(y/x) and this is why I am...
Thank you, tiny-tim. I usually use latex for big equations, but I thought it wouldn't be a big deal.
I was thinking that I could solve it like your wikipedia link... this will be interesting. Thanks.
Yes, I am aware that it is kinda difficult to solve for 'y' and that's why I wanted to try it out. It involves imaginary numbers and many roots.
If someone can point me in the right direction, that would great.
Homework Statement
When possible express the general solution in explicit form.
Solve dy/dx =x^2 /(1+y^2)
Homework Equations
This is a first order non-linear ordinary differential equation.
The Attempt at a Solution
dy(1+y^2) = x^2 dx
Integration both sides returns:
y+ (y^3 )/3=...
I know that the axis are rotate with respect of the x-y coordinates. I thought that the equation was still valid in these cases.
Yes. I see the xy term and I showed it in the first post. I am trying to compare it with 1, since it fits the equation. However, this equation would be wrong. I...
Homework Statement
(x+y)^2 + (y-2)^2 =4
2. Homework Equations
y^2 = (2-x)y - (x^2)/2
Equation of an ellipse:
##\left( \dfrac {x-h} {a}\right) ^{2}+\left( \dfrac {y-g} {b}\right) ^{2}=1##
From this, we know that (h,g) is the center of the ellipse.
and the radius along the x and y...
I didn't say that b1-b2=1, I meant that b1=b2=1.
So, supposedly since p|(b1-b2); b1-b2= kp, where k is an integer. Are they saying that it's impossible p | (b1-b2) , unless b1=b2 or in other words that p|0 or 0= pk, where k is any integer and in this case k=0?
Or are they saying that...
Homework Statement
Let p be an odd prime. A number ##a\in \mathbb{Z} _{p}^{\ast }## is a quadratic residue if the equation ##x^{2}=a\left( \mod p\right)## has a solution for the unknown x.
a. Show that there are exactly (p-1)/2 = quadratic residues, modulo p.
The Attempt at a Solution...
According to Wikipedia, Diophantine equations are written as follows:
ax + by = c
The Diphantine equation that you are really writing is this
35x-50n=10?
I understand everything, until you change the equation 1=7 -2(10-7)= 3(7)-2(10)=1. I understand that 21-20=1, but why changing from 7-...
I have read somewhere that division is not defined in modular arithmetic. Can someone tell me how this affect my solution?
@kru: This is puzzling, since I found those other solutions at a .edu site.
Homework Statement
Find all solutions to the equation ##35x\equiv 10mod50##
The Attempt at a Solution
gcd( 35,50)= 5
So, there is a solution to this, since 5| 10. Also, there is a theorem that guarantees the existence of exactly 5 solutions.
Now, dividing ##35x\equiv 10mod50## over...
Homework Statement
y= (x^2 -7) e^x
The Attempt at a Solution
I'm trying to find inflection points by setting the second derivative=0
I found that the derivative is:
##2xe^{x}+x^{2}e^{x}-7e^{x}=0##
##e^{x}[2x+x^{2}-7]=0##
Then, the 2nd derivative:
##e^{x}[(x-1)(x+5)]=0##, then the...
The denominator is never negative. It approaches 0 from the right hand side.
Is this the same as saying: (any constant)/ (a number infinitely small that never really reaches zero) ?
Then, it follows by the same principle as 1/ (x^2) as x->0 grows without bound?
I see that the numerator is approaching 2.333... and the denominator approaches 0.
I know that, when lim x-> 0 1/(x^2) it's very clear that the function grows without bounds, but in this occasion I just can't see how it grows.