# In a thesis, is it appropriate to allude to results obtained later on?

I want to provide a result in chapter 2, but formally prove this result in chapter 8.Can I say something like, "as we will see in chapter 8, this result in chapter 2 is true"?

# What does “get off the treadmill” in the content of this sentence?

It’s an exercise in frustration for
everyone involves, and it’s time to get off the treadmill.”
- Lost At School, Chapter 01

Is "get off the treadmill" a slang?

# how to change the chapter number in InDesign CS6

I have purchased an InDesign template, complete with text, headings, and chapter numbers.I have deleted chapters 2 - 8, and now I want to rename the text Chapter IX to Chapter II, but the text is not editable - it looks like it is a predefined section.

# What is the name of the chord in this cadence?

I am working through the Augmented Sixth Chords chapter of Piston's Harmony (5th Edition).The last figured bass exercise, 1g ends with the following cadence.

# A simple construction of a connected non-path-connected subgroup of a torus

In Structure and Geometry of Lie Groups by Hilgert and Neeb there is an exercise to construct a connected subgroup of $(\mathbb{R}/\mathbb{Z})^2$ which is not path connected (Exercise 9.Considering this is an exercise in a basic book on Lie groups (appearing in the first chapter on them!

# Applications of the Weak and Weak$^*$ topologies to PDEs?

Chapter $3$ of Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis constructs and explains the Weak and Weak$^*$ topologies over a Banach Space $E$.The most remarkable result of these topologies is the Banach-Alaoglu-Bourbaki, which asserts that for the weak$^*$ topology (Over $E^*$), the unit ball: $$B_{E^*}=\{f \in E^* | \ ||f|| \leq 1 \}$$ is compact.

# Projective but not free (exercise from Adkin - Weintraub) [closed]

This is exercise 38 from Chapter 3.Modules and Vector Spaces in Algebra by Adkins and Weintraub (GTM).

# Rudin's functional analysis exercise 4.21 - inequality typo?

In Rudin's Functional Analysis
Chapter 4 exercise 21, the last formula:

$$\textrm{Re}\, \sum_{n=1}^\infty \alpha_n \langle x_n, x^* \rangle \leq 1$$

Shouldn't the inequality be reversed?The whole exercise:

# Integration substitution, Curve Length

Length of curve $(t, \log t)$ from $1$ to $2$.This problem is from Lang's Calculus of Several Variables; chapter 2, subsection 2, exercise 5.

# Bourbaki exercise on intransitive relations

This the exercise 10 of chapter 2 of Bourbaki "Théorie des ensembles", whose intention is to generalize the correspondence between equivalence relations and partitions.3) For distinct elements $a$ and $b$ of $X$ such that $aRb$, we define $C(a,b)=\{x\in X:(aRx\wedge bRx)\}$.

# Spivak calculus chapter 3 problem 6 function

I am still working on Spivak calculus and at problem 6 of the third chapter, I came across an exercise that has been confusing me for a couple hours.I understand the solution (well, I understand how I got there but I have no idea what my solution represents).

# Exercise 4.a, Chapter 8, Resnick's A Probability Path

Show $X_n\Rightarrow X_0$, if and only iff, for every $k\geq 0$, $P[X_n=k]\rightarrow P[X_0=k]$.My work:

$P[X_n=k]\rightarrow P[X_0=k]$ implies $X_n\Rightarrow X_0$ due to Sheffe's Lemma (convergence of densities implies weak convergence).

# Baby Rudin Chapter 1 Problem 16

I am attempting to self-study through Baby Rudin and I have done every exercise in chapter 1 except for problem 16.Every solution I find on the internet for this problem uses theorems from linear algebra which I have no background in.