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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Resources to learn math proof for complete beginner

I've been looking up resources for learning to do math proofs. I come across resources that are advanced and covering techniques like 'prove by contradictions' etc. However, what I need is to first understand each and every arithmetic components in…
Wong
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Need a more elegant solution to proof

I've been working on a proof and this issue came up. Let's say I've made a claim that $ 7 \nmid 6x^2 + 13x - 5 $. It follows then that $ 7 \nmid (3x -1)(2x+5) $. But does it follow that $ 7 \nmid (3x-1) \wedge 7 \nmid (2x + 5) $? & also I have an…
tuba09
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Proving that $\frac{2n+1}{n+1}$ is not an integer for any $n>0$

As part of a proof I'm writing I want to prove that for any integer $n>0$, $\frac{2n+1}{n+1}$ is not an integer. I'm stuck on how to go about proving this -- I understand why it's true in my head but struggle to put it into words. I'll give it a go,…
werner_b
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I'm trying to prove $.\dot9 = 1$. What is wrong with this proof?

I am trying to prove that $.\dot 9 = 1$. I've come up with something that seems intuitively like a proof, but I believe it is structured incorrectly. Furthermore, it contains a term that is undefined. I think this "proof" may only intuitively prove…
user966422
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Why does contrapositive imply conditional?

Lets say P implies Q. Therefore I understand that ~Q implies ~P, because if Q is not true then P can never be true. However, I don’t get why it’s true the other way round. For example: If not B then not A, how do you get that A implies B from that…
Mohamed Shereef
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Prove $\forall m,n,p\in \mathbb{Z}:m=p\implies m+n=p+n$

My question is whether proving $\forall m,n,p\in \mathbb{Z}:m=p\implies m+n=p+n$ is equivalent to prove $\forall n,p\in \mathbb{Z}:p+n=p+n$ and if it is why?
user923938
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Standard logic notation in mathematics

My profesor is always complaining that my proofs are very long and difficult to read because I never use notation, meaning I say everything in words. Tired of that I decided to study logic by myself and develop my proofs by using the methods of…
Daniela Diaz
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Proof by enumeration/proof by exhaustion of integral expression

I am looking to prove my conjecture that \begin{equation} \int\cdots\int f(x_1,\dots,x_n) \,dx_1\cdots\,dx_n=I_n. \end{equation} over the domain $\{(x_1,\dots,x_n):0< x_1\leq\cdots\leq x_n<\infty\}$ where $I_n$ is some expression. Given that it is…
index
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Meaning of Isomorphism

In Hilton's A Course in Homological Algebra Page 21. $A$ is a ring with unit which is not necessarily commutative. Here is Propsition 3.4: Prop3.4: Let $B$ be an $A$-module and $\{A_{j}\}_{j\in J}$ be a family of $A$-modules. Then there is an…
richer_Ge
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Truth value of a statement

I have a problem: Let P be the statement " x $\in$ A and x $\in$ $\mathbb{Z}$ " statement: ($\forall$x)P $\Longrightarrow$ ($\exists$x)P Is there a set A for which the truth value of the above statement is false? Explain. My approach is: The…
hanamontana
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Using the word or in proofs

When using the word "or" in proofs, what if one of the statements is true and provides the correct justification that finishes the proof, and the other thing you state is either false or true but not always true? Would this mean that the proof is…
kevin firme
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Proving a quadratic equation identity

Continued question here I encountered this question: For quadratic polynomials such as $x^2\pm5x\pm6$ or $x^3\pm5x\mp6$, can be factorised over the integers. The main problem is to find a generator which can generate every polynomial that have this…
xxxx036
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Does the "$\neq$" in, for instance, "Prove that $(x+y)^2\neq x^2+y^2$" mean "never equal"? "not equivalent"?

I have the problem: Prove that $(x + y)^2 \not= x^2 + y^2$ I have answered it with something like this: $$(x+y)^2 = x^2 + 2xy + y^2$$ $$(x^2 + 2xy + y^2) - (x^2 + y^2) = 2xy$$ $$\therefore (x + y)^2 = x^2 + y^2 \Rightarrow 2xy = 0$$ $$\therefore…
OliverRadini
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Prove that $(n! +n) \leq (n+1)!$

How can I prove that $(n! +n) \leq (n+1)!$ given that $n \geq 0$?
choptxen
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Proving two sets E and G have no common elements

Say I have a set $E$ with an arbitrary number of elements which are of the form $f$ i.e. $E=\{f(x):x \in\Bbb N\}$ and a set $G$ with an arbitrary number of elements which are of the form $h$ i.e. $G=\{h(a):a\in\Bbb Z\}$. What would be the general…
Diamoniner12345
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