0
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0answers
3 views

Need help in algebra question

I hope u can help me out For number 8 and 9 find each value if f(x) = -3x^3 + 2x^2 8) f(-1) 9) f(1/2)
0
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0answers
3 views

Is a subobject classifier logically equivalent to set-inclusion?

Can one subsume the notion of set-inclusion $\subseteq$ and $\subset$ with the notion of a subobject classifier, expressed via an injective morphism $\hookrightarrow$? Specifically: Are the ...
0
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0answers
3 views

Bounding random variable

Let $y_1,...,y_k$ be random variables that get only 1 and 0 such that $P(y_i=1) \ge 2^{-1} +q$ for all $i$ and let $Y$ be the sum of all these variables. I want to bound $P(Y \le k/2)$ using chernoff ...
0
votes
0answers
13 views

why absolute value function is not differentiable at X=0?

They say that the right and left limit does not approach a definite value hence it does not satisfy the definition of derivative.But what does it mean verbally in terms of rate of change?
0
votes
0answers
3 views

Finite models for Systems of Incidence and Parallelism Axioms?

I'm reading Shafarevich's Basic Notions of Algebras, my question is at the end of these prints. I don't understand what's the connection of that linear equations (in the end of the ...
0
votes
1answer
5 views

Why is the equation $\frac{(z-i)^2}{(z^2+1)^2}=\frac{1}{(z+i)^2} $ in the residue theorem accurate?

I don't understand the reasoning here: $\frac{(z-i)^2}{(z^2+1)^2}=\frac{1}{(z+i)^2} $
1
vote
0answers
7 views

Extension field of finish degree

Let $E$ and $F$ two finish extension of a field $K$ of degree $[E:K]=m$ and $[F:K]=n$ such that $\gcd(m,n)=1$. Show that if $\alpha\in F$ has degree $r$ on $K$ therefore $\alpha$ has degree $r$ on ...
0
votes
1answer
9 views

Finding the maximum and minimum of sets

1) Does $[0, \sqrt{2}] \cap \mathbb{Q}$ have a minimum? Maximum? Minimum is $0$ since $0$ is also a rational number. $\sqrt{2}$ cannot be the maximum because it is not a rational number. How can I ...
1
vote
0answers
4 views

Equality of explicit recursively enumerable sets independent of ZF

Are there two recursively enumerable sets defined by explicit enumerators whose equality is independent of ZF? If so, can such sets each have finitely many elements? I don't know how exactly to define ...
0
votes
1answer
9 views

Write an equation in standard form for the line that is parallel to the graph of -8x= 5 - 4ynd has y-intercept -0.5

I hope somebody can help in my homework Question: Write an equation in standard form for the line that is parallel to the graph of $-8x= 5 - 4y $ and has y-intercept $-0.5$
1
vote
1answer
17 views

Let $p$ be a prime number. How I can simplify this expression

My question is: Let $p$ be a prime number. How I can simplify this expression: $$z=2∑_{j=0}^{2^{p-3}}C_{2^{p-2}}^{2j}2^{2^{p-2}-2j} 3^{j}$$ where $C_{2^{p-2}}^{2j}=((2^{p-2}!)/((2j)!(2^{p-2}-2j)!))$
0
votes
2answers
14 views

How to find a conserved quantity in this differential equation.

Consider the system $\ddot x = x^3 -x$, what is the method to follow to find a conserved quantity for this system? So far what I have is: $\dot x = y$ and $\dot y = x^3 - x$ and I can find the ...
0
votes
1answer
3 views

Problem with the answer of a basic ratio problem

Here is the solved example. The answer given is 175, but my calculation comes out to be 375. I thought that it was just a typo, but it has been written twice, so I'm not sure. What am I doing wrong?
1
vote
1answer
7 views

A question on nilpotent linear operator on finite dimensional vector space with dimension same as degree of nilpotency

Let $T$ be a nilpotent linear operator of index $n>1$ ($T^n$ is the null operator but $T^{n-1}$ is not ) on a vector space of dimension $n$ ; then how do we prove that there is no linear operator ...
0
votes
2answers
13 views

How to show that 1/4 is in the standard Cantor set?

I have studied the method that shows 1/4 belongs to the standard Cantor set, proving that it has only {0,2} as digits in its ternary expansion. But how can I do this in some other way?
0
votes
1answer
9 views

What is the length of the longest decreasing sequence in integer matrix?

Given a finite $m \times n$ matrix $M$ with all distinct integers, we travel it following two simple rules: The travel can start from any cell, say, $M[i,j]$. At each cell $M[i,j]$, it computes the ...
0
votes
0answers
14 views

If $x \in \{1,2,3, \cdots, 9\}$ and $f_n(x) =xxxx\cdots x($ n digits) then find the value of $f_n^2(3)+f_n(2)$

If $x \in \{1,2,3, \cdots, 9\}$ and $f_n(x) =xxxx\cdots x($ n digits) then find the value of $f_n^2(3)+f_n(2)$ If x =1, then $f_n(1) = ?$ Please suggest how to expand such series. Thanks
0
votes
0answers
14 views

Beautiful bent triangles

Xº yº Zº are angles of tight rope triangle ABC. A killer bully bent its sides one degree each. So he got a concave hexagon with (x-1), 181, y-1, 181, z-1, 181 as its angles (all degrees). Proving that ...
0
votes
3answers
16 views

Probability of $X = Y$ for a bivariate pdf

Can somebody explain to me why the probability of $X = Y$ is $0$ for a continuous bivariate pdf and not the integral of $f(x, x)$ over all possible $x$?
2
votes
2answers
11 views

Commutativity of special type of permutations

Let $p_1,p_2$ be permutations on the set $S=\{1,2,...,n \}$ and define $U_1:=\{k\in S:p_1(k)\ne k\}$ , similarly we can define $U_2$ . Now I can prove that if $U_1 \cap U_2=\phi$ , then ...
0
votes
0answers
21 views

How to show that the integral converge or diverge?

I have the following integral and wish to see whether it converge or diverge. where the integration contours $-l_1$ to $l_1$ belong to real numbers. I have tried by comparison test like the ...
0
votes
0answers
10 views

Basis of a set of vectors

Assume that we have a set of vectors as $S=\{v|v=(\sum_{i=r+1}^nx_ic^i_1,\dots,\sum_{i=r+1}^nx_ic^i_r,x_{r+1},\dots,x_n)^T,\forall x \in \mathbb{R}^{n-r}\}$. Here the first $r$ elements of the vector ...
0
votes
1answer
12 views

How is a coordinate system called where values increase to the bottom instead to the top?

In some computer graphics libraries the coordinate system is almost like the "usual" cartesian coordinate system. The only difference is that the $y$ values increas to the bottom, not to the top. ...
1
vote
0answers
11 views

A counting problem related to Parallelogram

There are n distinct points in the plane, given by their integer coordinates. Find the number of parallelograms whose vertices lie on these points. In other words, find the number of 4-element subsets ...
1
vote
0answers
26 views

Does $f ≥ g$ always imply $f^{-1} ≤ g^{-1}$ for invertible $f, g$?

If $I = (I, ≤)$ and $J = (J,≤)$ are linearly ordered sets, does $f ≥ g$ awalys imply $f^{-1} ≤ g^{-1}$ for invertible $f, g \colon I → J$? This is easy to prove if $f$ and $g$ are assumed to be ...
1
vote
0answers
10 views

Measurability properties of processes that arise as limits of sequences of measurable processes

I try to reduce my problem to a more general statement from which I want to know whether this is true in general. I have a sequence of continuous-time stochastic processes $X_t^{(n)}, t \geq 0$ with ...
2
votes
4answers
15 views

Simplifying expressions when taking limit to infinity

When taking the limit as $x$ approaches infinity of the function $[(x-2)^2+4x-x^2]/5$. How far should I simplify? I can simplify the part in parentheses, but simplifying further will get me $4/5$ and ...
0
votes
0answers
15 views

second order differential equations

Determine the longest interval in which the given initial value problem is certain to have a unique twice-di erentiable solution. Please do not solve the equation. (t-1)y''-3ty'+5y=sint y(-3) = 2 ...
0
votes
0answers
12 views

Any book on timeline of progress of Math concepts and applications

I was wondering if there is any book that chronicles the progress of Math over the centuries and also mentions about how/when applications of various theories were discovered/invented. I have been ...
1
vote
1answer
11 views

If $A$ is a convex set in $R^n$ with a limit point $x_0$, can we have a line segment in $A$ with $x_0$ its limit point…?

If $A$ is a convex set in $R^n$ with a limit point $x_0$ outside $A$ can we have a line segment in $A$ with $x_0$ its limit point...?
1
vote
0answers
8 views

Diagonalisable linear operator on infinite-dimensional vector space: definition problem

How to define a linear operator on an infinite-dimensional vector space to be diagonalisable? I have tried to search for the definition on internet but it seems not very fruitful as all are about ...
0
votes
2answers
24 views

Proof by induction with variable other than $n$

1) Prove that $(1+x)^{n} \geq 1 + nx$ for every $n \in \mathbb{N}$ and $x \in (-1, \infty)$ Base case: Usually for the base case I just take $n = 1$ but since there's another variable $x$, I wasn't ...
0
votes
1answer
11 views

Are prime ideals always comaximal?

This is easy to see in the ring of integers. In fact, the ideals don't even have to be prime. It's enough to be coprime. Then their GCD is 1, so 1 can be written as a linear combination of the ...
0
votes
2answers
26 views

$\int_0^\pi \tan(\theta + \text{i}a)\text{d}\theta$ =?

Solve the integration $$\int_0^\pi \tan(\theta + \text{i}a)\text{d}\theta$$ Where $a\in \mathbb R$ and $a \neq 0$ The method I took is to let $$z=e^{i\theta}$$ and since ...
0
votes
0answers
10 views

A simple arithmetic problem

In a field grass grows at uniform rate ; If the field can feed 36 cows for 4 days , 21 cows for 9 days , how many cows can be feed for 18 days ? My solution : Let $x$ be the initial amount of ...
1
vote
1answer
13 views

showing $\psi: R\to \mathbb C$ is ring isomorphism.

Below is an example from I.N. Herstein: Let $R=\Bigg\{\left( \begin{array}{ccc} a & b \\ -b & a \end{array} \right)\Bigg|a,b\in \mathbb R\Bigg\}$ and let $\mathbb C$ be the field of ...
-1
votes
1answer
12 views

series problem feedback needed

this is a example from my lecture notes and while studying i cannot understand how the final answer is found. the particular place where i am confused i have circled. shouldn't it be -1/n(n+1) ?
0
votes
1answer
21 views

Question on abstract algebra about invertiblity?

Let $(G,*)$ be a group. Could anyone give me an example $a,b\in G$ such that $$a*b=e ~ and ~ b*a\neq e $$ Where e is the identity element. I would appreciate any help. Thanks in advance!
0
votes
0answers
12 views

Attempted proof of expression for $p_2(n)$, the nth composite of two primes

This is an exercise to find an expression for the general 2-prime $p_2(n)$ from the generalized PNT. The 2-primes are numbers comprised of two primes factors, possibly repeated. The notation ...
0
votes
2answers
13 views

How can I evaluate this double integral by using geometry/symmetry?

I have to evalute this integral. $\displaystyle\iint\limits_{D}(2+x^2y^3 - y^2\sin x)\,dA$ $$D=\left \{ (x, y):\left | x \right |+\left | y \right | \leq 1\right \}$$ At first, I evaluated simply by ...
0
votes
0answers
10 views

Two surfaces that could be birational.

Suppose that $X$ and $Y$ are two non isomorphic non-singular complex projective surfaces. We also know that there is a morphism of varieties $f:X\longrightarrow Y$ which is bijective. At this point ...
1
vote
1answer
12 views

Magnitude of the value of a line at a point which does not lie on it

This may be trivial but I had never thought of it before. I know that the sign of the value represents on which side of a line a point lies but don't know what the magnitude of that value represents. ...
0
votes
1answer
22 views

Is $(\frac{1}{ x}\frac{d}{d x})^k(\frac{x}{\sinh x})$ always a bounded function?

Consider $f_{k}(x)=(\frac{1}{ x}\frac{d}{d x})^k(\frac{x}{\sinh x})$, $x>0$, $k=0,1,2,\cdots.$ Then, Is $f_{k}(x)$ always a bounded function? The only thing one need to care is the behavior when ...
-5
votes
1answer
44 views

what is The general sequence of: 1, 7, 12, 17, … [on hold]

i have an math question. what is The general sequence of beloow sequence? 1, 7, 12, 17, ... thanks
2
votes
1answer
15 views

A question about characteristic classes

I have a map $\phi:BO(1)^n\rightarrow BO(n)$ which is given by sending any $n$-tuple in $BO(1)^n$ to an $n$-plane through the origin. Thus, this induces a group action on the symmetric group $S_n$ ...
0
votes
0answers
14 views

Beautiful Geometric triangle roblem

Circle, inscribed in ABC, touches BC, CA, AB in points A', B', C'. AA' BB', CC' intersect at G. Circumcircle of GA'B' crosses the second time lines AC and BC at $ C_A $ and $ C_B$. Points $ A_B, A_C, ...
0
votes
1answer
24 views

Solve ${z_1/\overline{z_2}} = z^3$

Let $z_1,z_2$ be complex numbers such that: $$z_1= 4\sqrt{2}-i4\sqrt{2}$$ $$z_2= \cos{135^\circ} +i\sin{135^\circ}$$ Find all the complex numbers $z$ that fulfill the following equation: ...
0
votes
1answer
10 views

Proving congruence class

Let $a$ and $m$ be integers such that $m ≥ 1$. Consider the congruence class of $a$, $[a]$ modulo $m$. It follows that $∀ x ∈ [a], \gcd(x, m) = \gcd(a, m)$. I have my algebra midterm in two ...
-1
votes
1answer
21 views

Verify that 1+i = √2cos(45) + isin(45)

Verify that $1+i = \sqrt{2}(\cos45^\circ + i\sin45^\circ)$ and compute $(1+i)^{100}$.
0
votes
1answer
23 views

Beautiful logical minimum construction

On a circle after equal intervals 25 points are located. On every point is a policeman. All policemen are numbered (from 1 to 25) in some way. Now they have to move to some other points through this ...

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