# Tagged Questions

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### difference between n - 1 and n-1

I hope things are going well. I am doing some recursion stuff with databases and the text book I am reading has made it clear there is a difference between n-1 for example and n - 1. The difference ...
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### What does this log notation mean?

Can someone please explain what $^2\log x$ means? Is it the same as saying $\log x^2$ or is it something completely different? Here is an image of it as an example:
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### Is this notation good for the chain rule derivative?

When we take this derivative, for example: $$y = \log(\sin x)$$ We call $u = \sin x$, so we have: $$\frac{dy}{dx} = \frac{d y}{du}\frac{du}{dx} = \frac{1}{u}\cos x = \frac{\cos x}{\sin x}$$ But for ...
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### problems on define set with polynomials

I'm trying to say set A is the set of nonnegative integers that not of this two forms $3x^2 + (6y-4)x - y\$ and $\ 3x^2 + (6y-2)x + (y - 1)$, for example: $4=3 \cdot1^2+(6 \cdot1-4) \cdot 1-1\$ is ...
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### Notation for Derivatives with Respect to Time

My math teacher writes $\frac{dx}{dt}$ as $x'$, and makes us do the same for homework. (in a particle motion context, where $t$ is time) I am aware that the standard notation is usually $\dot{x}$, ...
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### Representing trees in Set builder notation?

Is there a way to represent graphs and minimum spanning trees using set builder notation? e.g. I have a weighted graph of n nodes, all connected to each other in a mesh network manner. I am to ...
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### Groups - Compositions

If the f is written to the right of its argument does that mean the composition of $f g$ is actually $g(f(x))$ instead of being $f(g(x))$ which is the notation I'm used to. I ask this because I read ...
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### Is this a good expression of the claim using logical notation?

Four Square Theorem: Every positive integer can be written as a sum of four integer squares. Expressed in logical notation : $$\forall n>0 =a_{0}^{2} + a_{1}^{2} + a_{2}^{2} + a_{3}^{2}$$
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### Surprised over notation in fundamental theorem

So I'm looking into the fundamental theorem of calculus and I'm a bit weirded out by the notation used in part two. $$\int_{a}^b f(t) dt = G(B)-G(a)$$ Why don't we say $F(b)-F(a)$? We are just ...
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I have the following expression $$\partial_k\sigma_{ik} = \partial_i\partial_ku_k + \partial_k^2u_i$$ I know that a repeated index means summation. So for a 2D space $(x, y)$ I would get (for the ...
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### What does $\alpha+\gamma$ mean when $\alpha$ and $\gamma$ are well-ordered sets?

I was asked to prove the following: let $\gamma$ be a well ordered set with the following property: for any $\alpha$ and $\beta$ well ordered sets, if $\alpha+\gamma=\beta+\gamma$ then ...
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### What is this strange symbol called :=?

I want to Google it but I don't even know what to call it. It looks like some sort of assignment used in computer science or math. Here it is again := It is ...
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### Atiyah-MacDonald 5.10

The problem says: Let $f:A\rightarrow B$ be a ring homomorphism and let $f^{*}:\operatorname{Spec}(B)\rightarrow \operatorname{Spec}(A)$ be the mapping associated with $f$. And then comes the ...
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### Tree graph intuition + mathematical notation

Let $T$ be a tree with at least two vertices. Consider a path of maximal length in $T$. Prove that the start and end point of this path have degree 1 by contradiction : If we let the start and ...
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### How can this algorithm be expressed in mathematical terms?

I have found a solution to a basic problem using an algorithm, but I'm having a bit of a hard time expressing this algorithm in terms of discrete math. ...
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### little o notation with natural logs

I'm having trouble with little o notation. Help me show that: $2(n^2 + 100n)\log^5n = o(n^2\sqrt{n})$. It is the last hwk on my sheet and I don't understand it, if someone can help me with ...
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### Is this a correct translation from recursive function to math notation?

I have this recursive function, written in Java. Assignment is to translate it to mathematical notation. ...
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### What is '+' in set notation

In set $T = \{(0+2)^{i+5}|\space i \in \mathbb{N}\}$, what is the meaning of the $(0+2)^{i+5}$?
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### Field extensions, inverse limits, notation and roots of unity

I'm hoping I can get some assistance with a revision problem and also a notational issue I'm not sure about (although it may not be standard). I seem to remember going over this or something similar ...
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### Disproving a big O equation

As a homework assignment I am trying to prove/disprove the next statement: Let $f(x)=O_a(g(x))$, then $\forall A,B\in\mathbb{R}\rightarrow A\cdot f(x)=O_a(B \cdot g(x))$ Which I think is wrong ...
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### Notation : What is the meaning of the (mod n) in factoring algorithms?

Pretty much every thing is in the title, really! I'm trying to come up with an efficient algorithm to factorize large integer as an homework for a parallel programming course. I've seen a few pages ...
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### Sequence Notation

I have come across the following in the book "Principles of Program Analysis" by Nielson, Nielson and Hankin to represent a sequence and I am unsure of what its constituent parts mean. Obviously ...
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### $(fg)(x)$ and $f(g(x))$. Commutability in Limits

Is there a difference between $(fg)(x)$ and $f(g(x))$? From my lecture slides $\lim\limits_{x\to a} (f(x)+g(x)) = \lim\limits_{x\to a} f(x) + \lim\limits_{x\to a} g(x)$ Then in the next slide, it ...
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### Question Concerning The Solution Of A Differential Equation

Here's another question from Advanced Engineering Mathematics by Greenberg [Ex 1.2 Q5]: For what values of the constant $\lambda$ will $y = \exp(\lambda x)$ be a solution of the differential ...
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### Understanding the $\equiv$ symbol

I am trying to understand a wierd symbol in a book and I am failing. The symbol is this '$\equiv$'. I understood that if I have $32\equiv 2\bmod15$ means that if I divide $32$ with $15$ I will get ...
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### What is the “limit point of a function?”

I am asked to prove that Show that a sequence $x: \mathbb{N} \to \mathbb{R}$ has a limit point iff there $\lim_{n\to\infty} x(n)$ exists as a limit point of a function from a subset of metric ...
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### What is the meaning of a small o in between function names? i.e (f o g)

I am helping with homework. I am stumped here - What is the meaning of the small round circle, or small "o" in question 19 (that I underlined) and question 20
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### Interval Notation With Gaps

I have $A = (-10, -4)$ and $B = (3, 8)$. And I am trying to write the answer to $A \cup B$. I know the answer is $(-10, -4)$ and $(3, 8)$ but I am unsure how to write an interval range where there is ...
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### Cover & Thomas textbook notation

Exercise 2.27 in Elements of Information Theory (2nd ed.) reads: Let $\mathbf{p} = (p_{1}, p_{2}, \ldots, p_{m})$ be a probability distribution on $m$ elements (i.e., $p_{i} \geq 0$ and ...
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### PEDMAS in RPN needed?

In RPN do we still have to take into note the PEDMAS rules? For example these questions: 3 – 4 * 2 3 * 4 – 2 3 * (4 – 2) (3 – 4) * 2 3 – 4 + 2 Answers 342*- ...
Let $f(n) = n^3(5+2\cos(2n))$ and $g(n) = 3n^2+4n^3+5n$. Given these two functions, I must determine the appropriate symbol where the underscore is: $f(n) \in \_(g(n))$ So, first thing to do is take ...
A problem in Dummit and Foote states: Let $k$ be a field and let $k(x)$ be the field of rational functions in $x$ with coefficients from $k$. Let $t \in k(x)$ be the rational function ...