# Questions tagged [proof-writing]

For questions about the formulation of a proof. This tag should not be the only tag for a question and should not be used to ask for a proof of a statement.

15,866 questions
Filter by
Sorted by
Tagged with
54 views

### Proving that a set of three quadratic equations in three variables always has a solution

Given the following system of equations in $s, t, r$: $$t^2 + s^2 - 2 t s \cos(\theta_1) = a^2$$ $$s^2 + r^2 - 2 r s \cos(\theta_2) = a^2$$ $$r^2 + t^2 - 2 r t \cos(\theta_3) = a^2$$ How can I ...
• 24.4k
1 vote
59 views

### Prove $\frac{d}{dx} \frac{f(x)-f(a)}{x-a} \geq 0$ if $f(x)$ is convex without twice differentiability.

I've recently been trying to understand some proofs about convex functions. The definition of convex I'm using is: Let $f(x)$ be a once differentiable function defined on $[a, b]$. $f$ is convex iff ...
• 409
130 views

### Is implication true if two statements are always the case?

I have a task that requires me to show that under a certain set of circumstances, a set has property A if and only if it has property B. I can show that under the given circumstances, the set always ...
• 15
1 vote
62 views

### Choosing the Starting Point of Induction

I am a self-study student learning the basics of math proofs. During my studies, I encountered the following question: (For all n $\ge$ 3) I completed the problem using weak induction (with a ...
• 121
39 views

### Permanent divisor in highly composite numbers

I was wondering whether it is true that if a particular divisor (be it prime or composite) appears for the first time in the sequence of highly composite numbers (HCNs), would it still be present for ...
• 456
1 vote
62 views

1 vote
35 views

### Prove: If $f_1$ and $f_2$ are integrable, then $f_1\vee f_2$ is integrable over each $A\in\mathscr{A}$.

I need to prove the following result: Let $(X,\mathscr{A},\mu)$ be a measure space. If $f_1$ and $f_2$ are integrable, then $f_1\vee f_2$ is integrable over each $A\in\mathscr{A}$. Here is my ...
• 2,483
91 views

59 views

### Maximum function recursive property

In an old book by Richard Bellman, I found a proof of the initial Bellman equation: $$f_n(x)=\max_{0\le x_N\le x}\left[g_N(x_N)+f_{N-1}(x-x_N)\right]$$ where $x_i\ge 0$ and $\sum_{i=1}^Nx_i=x$. ...
22 views

### Feedback on and assistance with this proof about a particular quotient space of $\mathbb{C}P^1$

The goal here is to define the particular equivalence relation I'm attempting to describe, and then provide an equation (in this case, (2)) that can be used to determine whether or not two given ...
• 887
47 views

5k views

### Are there statements so self-evident that writing a proof for them is meaningless? Is this an example of one?

Context: I know nothing about proofs and only a small amount about formal logic used in proofs. I'm trying to learn the basics of how to write a proof. For example, suppose I wanted to prove that &...
• 419
144 views

### Help me to verify the proof of this theorem, which is proving $k$ª $=$ $\prod_{i=1} ^{\infty}$ $\mathbf K_{p_i}$ by using maximality and minimality

I want to verify my proof is true or false. The exercise what I want to prove is under theorem. $\mathbf {Exercise}$: Let $\mathbf k$ be some perfect field and $\mathbf K_{p_i}$ is a compositum of ...
52 views

I am self-studying signed measure, and I come across the following construction: Let $\mu$ be a signed measure on the measurable space $(X,\mathscr{A})$, and let $A$ be a subset of $X$ that belongs ...
• 2,483
57 views

### How much notation should there be in a formal proof? Is there a general guideline?

I am writing a conference paper in formal language theory with an involved proof and I've found myself struggling with notation. In particular, I don't know when to favor notation and when to favor ...
• 31
23 views

### How Does One Show That A R.V Has CDF F?

I'm self studying probability using Statistics 101 book. In chapter 3 there's a question(ex. 9): Let F1 and F2 be CDFs, 0 <p< 1, and F(x) = pF1(x) + (1 − p)F2(x) for all x. (a) Show directly ...
1 vote