# Tagged Questions

The process of studying mathematics without formal instruction. _Don't_ use this tag just because you were self-studying when you came across the mathematical question you're asking; it is only for when the fact that you're self-studying is what your question is _about_.

89 views

### How to avoid losing the woods for the trees in daily study/lecture time

When facing to some new material in mathematics, I feel easily to be overwhelmed by lots of details with losing the woods for the trees. So is there some good strategy to study the materials ...
211 views

### Uncountable Dense Linear Orders

Is there an example of two uncountable equipollent dense linear orders without endpoints that don't satisfy the same first order properties? Or is it true that two uncountable equipollent dense linear ...
135 views

36 views

### Limit with terms very similar to those that should give an exponential function

I have been trying to solve the following limit but am completely stuck. $$\lim_{\alpha \rightarrow \infty} 1-\left( \frac{y+\alpha}{\alpha-1} \right)^{-\alpha}$$ I have tried inverting the ratio ...
507 views

### Posterior Probability

a) Your initial belief is that a defendant in a court case is guilty with probability 0.5. A witness comes forward claiming he saw the defendant committed the crime. You know the witness is not ...
37 views

### Confusion about the associative property and the mechanics of Parenthesis

This is a follow up question on my earlier post (Updated): Showing that a set $M$ with two elements classifies as a field. I feel this post is necessary because I realize that what confuses me is how ...
42 views

### Simple probability question

Question: In class of 125 students, in examination 70 students passed in mathematics and 55 students passed in statistics and 30 passed in both the subject. Find the probability of the event where ...
40 views

### (Updated): Showing that a set $M$ with two elements classifies as a field

My question is more conceptual, so I will come straight to the exercise: Exercise: Let $M= \lbrace g,u \rbrace$ be a Set. On $M$ the Addition and the Multiplication is given by: \begin{align} ...
184 views

### Constructive proof for existence of integer part of real number

I try to prove de following exercise of my analysis textbook. Show that for every real number $x$ there is exactly one integer $N$ such that $N \le x < N + 1$. I have been finding a ...
126 views

### Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$

Any hints on how I can prove the inequality: $$|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$$ Thank you.
41 views

### Is this derivative correct?

I'm newbie at Calculus, so I'm doing some exercises of derivates, I know by the formula: $f(x) = \sqrt u$ $\frac {df(x)}{dx} = \frac{u'}{2 \sqrt u}$ that the derivate of the next function is: ...
80 views

### Question about Lebesgue Covering Dimension

Suppose we have a metric space equipped with two different metrics: $(X,d), (X, d')$. What must be true of the metrics: $d, d'$ in order for $X$ to have the same Lebesgue covering dimension? A ...
47 views

### Proof on existence of the natural numbers, crucial step.

I am trying to understand/reconstruct the proof given by my Professor addressing the existence of natural numbers. However there is one step in particular I don't understand and the more I think about ...
604 views

### Without solving the equation, determine the nature of its roots: $x^2 + ax + a^2 = 0$

I'm working through the book Core Maths for Advanced Level on my own, and, after solving the above problem, I'm not getting the same answer as the book. So, given: $$x^2 + ax + a^2 = 0$$ Using the ...
46 views

### Want to check measure theory proof

I need to show that sigma-finiteness implies semifinite. Does the following proof work? Let $(X,m,\mu)$ be a $\sigma-$finite measure. Let, $E\in m$, and $\mu(E)=\infty$. By $\sigma-$finiteness, ...
565 views

### Probably of 2 six in 5 dice rolls

What is the probability of obtaining exatcly 2 six when rolling a dice 5 times? In order to obtain this probability, I will need to devide the number of favorable events by the number of possible ...
93 views

### An exercise on first order logic formulas, terms and Polish notation

This is part of my homework (not mandatory and not accredited). Please comment/answer if my reasoning for the exercises is correct, because I'd like to see if I understand the material. I will start ...
45 views

### problem with rudin theorem 1.14 first step $g^{-1}((\alpha, \infty]=\cup_{n=1}^\infty f_n^{-1}((\alpha, \infty])$

Theorem 1.14 of Complex and real analysis by Rudin states: if $f_n:X\to [-\infty, +\infty]$ is measurable for $n = 1,2,3...$ and: $$g=\sup_{n\geq 1} f_n,~~~~h=\limsup_{n\to \infty} f_n,$$ then $h$ ...
72 views

### Show expectation is infinite

Let $X_1,\ldots,X_n$ be independent, identically distributed with expectation 1 and finite variance. Find the limit distribution of $\sqrt{n}(\bar{X}_n^{-1}-1)$. If the random variables are sampled ...
109 views

### The Use of Sound in Mathematics. [closed]

I'm not sure that this question is appropriate here. There's a good chance it's too opinion-based. If that's the case, I'm sorry. I was sat in a research seminar recently and wondered whether it'd be ...
545 views

### Proving, that closure of set is equal this set iff set is closed

I've started intorduction to topology course and I need help with one of the problems: Let $A \subset(X,T).$ Prove that $cl(A) = A\iff A$ is closed. It may looks trivial, but I had a little ...
33 views

### Definition of $C^1$ functions with values in $\mathbb R^m$

My analysis textbook defines a $C^1$ function $f:\mathbb{R^n}\to\mathbb{R^m}$ as one in which for each component function $f_i, 1\leq i\leq m$ the partial derivative $\frac{\partial f_i}{x_j}$ exists ...
140 views

### Path to 3d Mathematics programming, where to start?

This might read like duplicate of this question https://math.stackexchange.com/search?q=where+to+start However since that one wasn't answered, and I have a more specific problem in regards to ...