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Mathematics Stack Exchange

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.

Questions with this tag are about the presentation of a mathematical proof. Questions might include:

  • Should I include [x-mathematical detail] at [y-part of this proof]?
  • Is the following a sufficient proof of [x-mathematical tidbit]?
  • I have written the following proof, could I somehow improve it, does it have good flow/can I improve readability?

But this tag is not for asking someone else to write a proof for you, or for how to answer some question. Questions such as: My professor asked me to prove the Pythagorean theorem and I don't know how to begin are not to have this tag.

This tag is intended for use along with other, more "mathematical" tags. A question about the writing of a proof in abstract algebra, for example, should have as well. This tag can be used along with the proof verification tag.

See here for a useful set of guidelines for writing a solution.

15776 questions
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How would I mathematically prove that 1+1=2?

Everyone knows that 1+1=2, but how would one mathematically prove that this equation is true? Or can you?
user643243
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Show that $\log_e (n+a)- \log_e (n-a)=2(\frac{a}{n}+\frac{a^3}{3n^3}+\frac{a^5}{5n^5}+\cdots )$

I adopted this problem from higher algebra book by hall and knight pg.no 196 problem no. 3. I can't derive the proof.
Archit Pasayat
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I have a question regarding the use of dummy variables in a proof.

Lets look at the following question. Why would the proof be incorrect? Let U be any set. Prove that there exists an $A \in \mathcal{P}(U)$ such that for every $B \in \mathcal{P}(U)$, $A \cap B = B$. Proof. Our goal is $\exists A \in…
fesodes
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Would it be acceptable to define something the wrong way first, and then redefine it after showing why the first definition is insufficient?

Suppose I am writing an article or a book wherein I wish to introduce a mathematical object O. There is an intuitive image I have in mind when thinking about object O, and this intuitive image lends itself to an obvious sounding definition. However,…
Robly18
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Does this equal symbol make sense?

Sorry about the title not being that clear, but I wouldn't know how to summarize it. My question is a simple one, but it's been bugging me for a while. In bayesian probability, quite often, we consider the probability density function $f : x \mapsto…
Azur
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Face-Gauss Divergence Theorem proof

How one can proof that $\int_{\Omega}\nabla \mathbf{u} \cdot \mathbf{t} \,d\Omega = (\oint_{\partial\Omega}\mathbf{u} \otimes \mathbf{m} \,dL) \cdot \mathbf{t}$, where $\mathbf{u}$ is a vector field, $\Omega$ a polygon (i.e., flat and has…
Caslu
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How to prove $\int_{0}^{\frac{\pi}{2}}e^{-R\sin x}dx$ < $\bigl(\frac{\pi}{2R}\bigr)(1-e^{-R})$, for all $ R > 0$.

Hi sorry for bothering you, I encountered some problems while solving the following question, hope you can give me some advice of my method or any other ideas to figure out how to prove it. Thanks a lot. $R$ is an arbitrary real number, prove…
Yu Tien
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What do we call $P \rightarrow \lnot Q$?

Let us assume that we have a statement $P \rightarrow Q$. In this case, what would $P \rightarrow \lnot Q$ be called? The reason why I want to know is that I want to show that $P$ is true by contradiction, proving that both $\lnot P \rightarrow…
J.M.W Turner
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Formulating the proof in case of $\mathbb{R}$(1-dimensional)

Here is the proof in multiple dimensions Why does a Lipschitz function $f:\mathbb{R}^d\to\mathbb{R}^d$ map measure zero sets to measure zero sets? Here is my trial in 1-dimensional i.e. $f \in Lip[0,1],$ but I am unable to complete: Let $f \in…
Intuition
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Prove that the set $\mathcal{O} $ is absolutely continuous.

If $\mathcal{O}$ denote the collection of real-valued functions defined on $[0,1]$ that map every set of measure zero to a set of measure 0. Prove that the set $\mathcal{O} $ is absolutely continuous. could anyone give me a hint for the proof?
Intuition
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How to prove a statement about covering a set?

How to prove this statement? "Any set of measure $0$ can be covered by a sequence $((a_n,b_n))$ of intervals with $\sum (b_n-a_n) <\epsilon$." It seems like this statement is correct by intuition. but I do not know how to prove it, could anyone…
Emptymind
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How to write this argument more easy for reading?

I'm trying to show that $\mu_1 = \mu_2 = 0$ in the below system: $$\begin{cases} x \mu_1 &= 0\\ y(\mu_1 + \mu_2) &= 0 \\ z \mu_2 &= 0 \\ x^2 + y^2 &= 1\\ y^2+z^2 &= 4 \end{cases}$$ $\textbf{My attempt:}$ If $\mu_1 \neq 0$ then $x=0$. It follows…
Akira
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Finding the pre-image $f^{-1}(T)$ for $T = [4, 9)$ and $f(x) = x^2$

This is a homework question. My class is titled "Formal Mathematical Reasoning and Writing" and we are using Lay's Analysis with an Introduction to Proof. My question comes from section 7: Functions. Define $f:R \to R$ by $f(x)=x^2$. Find…
Ben Anderson
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Proof of corollary

I have a theorem that I want to break down into a theorem and a corollary to make my paper more readable. Can I use objects, e.g. a complicated set, that is introduced in the proof of the theorem in the proof of the corollary, or is this considered…
user98563
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Why does some proof require equality on all points, while some proofs suffices to check it a arbitrary points?

For example, here is an excerpt from "Introduction to manifolds" by loring W. Tu 20.4. If X and Y are smooth vector fields on a manifold M, then the Lie derivative $\ \mathcal{L}_XY$ coincides with the Lie bracket [X,Y]. Proof. It suffices to check…
folo polo
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