Mathematics Stack Exchange
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.

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Struggling with a proof when $x > 0, x > a$, then $x > a$

This is coming from a question in spivak's calculus, solving $(x-1)(x-3) > 0$. There are two cases where this is true, when both brackets are positive, or when both are negative. But when I look at the positive case, I get $x>1, x> 3$. I know…
Tomas
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Using the method of induction

Can someone help solve this problem? Prove that if $n≥1$ and $a_1,a_2,….,a_n$ are any real numbers, then $|a_1+a_2+⋯+a_n |≤|a_1 |+|a_2 |+⋯+|a_n |$.
Kell
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Name for proof by logical equivalence

A discussion on ELU stackexchange has led to the question of whether there is a name for the style of proof in which you start with the proposition to be proven and then proceed via a chain of logically equivalent paraphrases to—in the example…
Daniel Harbour
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Need help proving the following:

Any help at all would be great. Thank you very much. For all $m,n,p \in \mathbb{Z}$, If $p<0$ and $mp
user3182252
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Need help with a math proof

Any help would be greatly appreciated. Let $m,n,p,q \in \mathbb{Z}$. If $0 < m < n$ and $0 < p < q$ then $mp < nq$.
user3182252
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Formal expression for a proof

Yesterday I asked this question: Given: $f$ is Riemann integrable on $[a,b]$ and $f(x)\geq 0$ for all $x$. Prove that if \begin{equation} \int_a^b f(x) dx=0 \end{equation} and $f$ is continuous, then $f(x)=0$ for all $x$. Voldemort gave…
kiwifruit
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Prove as a direct theorem.

One of the question from my text book, it give a theorem and says that prove it as a direct theorem. For two statements A and B, the direct theorem is "if A is true, then B is true." In this case, is it possible to prove this theorem by using…
eChung00
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How should the sequence or list $k+1, k+2, \ldots, m$ be interpreted in a proof when $k \ge m$?

How should the sequence or list $k+1, k+2, \ldots, m$ be interpreted in a proof when $k \ge m$ ? Context: Suppose the matrix $K$ ($m \times i$) has $k$ pivots and let $q$ be the first column of the matrix $L$ ($m \times n-i$). If $q_{k+1}, q_{k+2}…
Shuzheng
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what conditions to take while proving a result.

Suppose I have a theorem's statement as follows: If statement A and statement B, then statement C. I want to prove the converse, but quite confused what conditions to consider. I got hint as follows: Given statement C and statement A, then prove…
monalisa
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Is this true? $(1+1/n)^n=1+1/1!+1/2!+1/3!+1/4!+\cdots + 1/n!$

Is this true? $$\left(1+\frac{1}{n}\right)^n=1+1/1!+1/2!+1/3!+1/4!+1/5!+\cdots $$($n$ times) or ($n+1$ times)? If yes how to prove it and were there any proof of it?
user123456789
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Math Proof Help

So I am supposed to add some condition to the original proposition to make it true but I do not know what condition I need to add. Original Proposition: If $x$ and $y$ are real numbers and $xy>0$, then: $$(x+y)/2≥√xy$$ Proof: Let us assume the…
user111702
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Bi-implication theorem proving

While proving a theorem, i came across a situation like as follows (P has a property) $\leftrightarrow $ $(x=y)$ (P has a property) $\leftrightarrow $ $(y=z)$ Now can i infer the following fact from the above two facts ? (P has a property)…
hanugm
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How to prove this is true?

The question is: Show that $$\log_2(n!)\in O(n \log_2(n)).$$ I'm guessing I'll have to use principle of simple induction for this one. But how would I go about writing the proof for this? Should I use proof by cases? What will be my first…
muros
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Proving $n^n \ge n!$, is induction necesary?

I am trying to prove that: $n^n \geq n!$ is valid for a $x$ set of numbers. So, I am trying an inductive process. However, case $P(0)$ doesn't seem to work because I have read somewhere that $0^0$ is undefined, but I've also read that $0^0$ is…
JOX
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Proving Characteristic Function

I tried looking at some of the questions that could apply, but I'm not sure that they applied to this type of problem. Given $A \in \mathcal{P}(X)$ define the characteristic function $ \mathcal{X}_{A}:X\rightarrow \{0,1\}$ by $$\mathcal{X}_A(x) =…
Daniel Cazares
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