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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Prove that there is no rational number whose square is 12.

Let's assume that $12 = (\frac{p}{q})$, where p,q $\in$ $\mathbb{R}$ and $p$ and $q$ are coprime. Then we have, $(\frac{p^2}{q^2})= 12^2 = 144.$ So, $p^2 = 144*q^2$ and $p^2 = 2*(72)*q^2.$ This implies that p is even. Then,…
Skm
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The identity element in multiplication

Let's get on with the question. Is it true that the multiplication is always commutative when we multiply an entity (number, matrix etc.) with the identity entity? I mean, the statement is true in the scope of numbers ($a×1=1×a=a$) and even in the…
Anonymus
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Prove every nonzero integer has only finitely many divisors

Prove every nonzero integer has only finitely many divisors axiom: For $d,n \in \mathbb{Z}$, if $d \mid n$, there $\exists k \in \mathbb{Z}$ such that $d \cdot k = n$ $\forall d > n, \,\, k = \frac nd = \notin \mathbb{Z}$ $\forall d < -n, \,\, k…
Bucephalus
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Prove that every number is divisible by $1$ and that the only numbers that divide $1$ are $1$ and $-1$

Prove that every number is divisible by $1$ and that the only numbers that divide $1$ are $1$ and $-1$ axiom: if $d \mid n, \, \exists k \in \mathbb{Z}$ such that $d \cdot k = n$ for $1 \cdot k = n, \forall n \,\exists k$ such that $k = n…
Bucephalus
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Prove that for $d, n \in \mathbb{Z}$, if for some nonzero integer $a$ we have $ad\mid an$, then $d\mid n$.

Prove that for $d,n\in \mathbb{Z}$, if for some nonzero integer $a$ we have $ad\mid an$, then $d\mid n$. Conversely, if $d\mid n$, then $ad\mid an$ for all $a \in \mathbb{Z}$. For the first part, I got: If $ad\mid an$, then $\exists k \in…
Bucephalus
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Help with proof involving field axioms of real numbers

I need help with this proof. If $a\ne0$ then $(a^{-1})^{-1}=a$ Which axiom do I use and what is $(a^{-1})^{-1}$ equal to. I tried this but I'm stuck $(a^{-1})^{-1}=(\frac{1}{a})^{-1}$ What comes next? Thanks a lot in advance!
Andres Romero
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Terminology for $x=-x$ when x is a positive integer

My proof by contradiction ends with $x=-x$ when x is a positive integer. What is the correct terminology for why this is a contradiction? Right now it says "This yields a contradiction since a positive integer cannot equal the negative value of…
GiantDuck
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Are vertical dots rigorous?

If I'm doing a proof and I use vertical dots or specifically say something like "carrying on in this way until", is that considered a rigorous proof? Here's a relatively simple example of what I mean from group theory. Let's say I want to prove…
Dylan
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3 different proofs

The question is: Given two permutation of $n$ natural numbers,what linear combination of them will have the most value? And we are asked to provide 3 different proofs. My 2 proofs: 1)suppose we have 2 $ n$ dimensional vectors,whose coordiante…
Logan Luther
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Proof: The difference between the product of two distinct prime numbers and their sum must be odd.

Prove: The difference between the product of two distinct prime numbers and their sum must be odd. I attempted to disprove the hypothesis by finding two distinct primes: $i, k$ where $(i \cdot k ) - (i - k) \equiv 2n $ As I have not been able to…
Bayyls
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Elementary set theory z

A ∩ (B ∪C) ⊂ B ∪ (A ∩C) Can anyone give me a general outline of an approach to take to this proof? I Don't really know where to begin.
user425137
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Proving that $c$ is the mean proportional between $a$ and $b$.

If $a≠b$ and $a:b$ is the duplicate ratio of $(a+c):(b+c)$, prove that $c$ is the mean proportional between $a$ and $b$. My attempt: I have assumed that $c$ is the mean proportional between $a$ and $b$, expressed $a$ and $c$ in terms of $b$ and…
MrAP
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Prove by contradiction that for every positive integer $k$, there is an integer $m$ such that $k\leq m^2\leq2k$

Prove by contradiction that for every positive integer $k$, there is an integer $m$ such that $k\leq m^2\leq2k$. Heres what I've done. Take the negation of the statement above to attempt a contradiction. We have "There exist a positive integer $k$…
Yellow Skies
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Proof using Division Algorithm where divisor is the least element of the set $S$ = {$ma + nb$ : $m,n \in \mathbb{Z}$ and $ma + nb > 0$}

Required To Prove: Let $a$ and $b$ be integers. Let $S$ = {$ma + nb$ : $m,n \in \mathbb{Z}$ and $ma + nb > 0$}, and $d$ be the least element. Show that $d$|$a$. The following is how I attempted my proof: Consider $d$ is not a divisor of $a$, i.e.…
Xandru Mifsud
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Pigenhole Principle Problem

I am doing some hw but I cannot figure out this one. Hint: it is part of a pigeonhole principle. Question: Prove that if $a$ is a natural number, then there exist two unequal natural numbers $k$ and $l$ for which $a^k - a^l$ is divisible by 10.…
Tsangares
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