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.

15776 questions
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Prove $w \in \mathbb{z} : k \mod 2 \neq 0 \rightarrow k \in \mathbb{z} : k^3 \mod 2 \neq 0$ directly

Prove $$ k \in \mathbb{Z}: {k}\mod{2} \neq 0 \rightarrow k \in \mathbb{Z} : k^3 \mod 2 \neq 0$$ using direct proof. I would like to prove that if integer $k$ is not divisible by 2 it implies that $k^3$ is not divisible by 2 either. Could someone…
Tuki
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How many Rooks on a chess board - 1 threatens at the most 2

On a chessboard with 8 × 8 squares a rook threatens all the chess pieces in the the same line or the same column in which it stands, regardless of whether another rook stands in between or not!! How many rooks can be placed on the chessboard…
calculatormathematical
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Proving for every real number on interval with trig

I understand that with questions asking you to prove for x on an interval requires induction. The question I have is: prove that for every real number $x \in \left[0,\dfrac{\pi}{2}\right]$, $\sin(x)+\cos(x)\ge1$. The base case is obvious: 0…
user2793618
  • 49
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How to write a proof with the use of $\propto$

I have an issue of style, for example with Bayesian stats: \begin{align} h(\theta|X) &\propto f(X|\theta) \pi(\theta)\\ & = \theta(1-\theta) . 2\theta & \text{(should I use '$=$' or '$\propto$' here if this is just a substitution?)}\\ & \propto…
polyglot
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Which way of formulating a proposition in an article is better?

Which of the following ways is preferable to formulate a proposition including much uncommon notation? 1) [half-page description of the notation in style "Consider projections of similar convex polyhedrons to a plane, orthogonal to S. Define…
Galtulling
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Why does the simpler way to computing the Gini coefficient work?

The Gini coefficient is often used in economics to calculate inequality. According to this website, the formula for calculating Gini coefficient is $G = \frac{\sum_{i=1}^{n} \sum_{j=1}^{n} |x_i - x_j|}{2n^2\bar{x}}$ However, if all values are…
wwl
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Is it possible to combine two different proof technique?

When I'm proving some problems, am I allowed to use two different proof technique to prove a problem? For instance, let's say I decided to do proof by contradiction on certain algorithm. Since algorithm has a pattern, I am thinking of using…
selfPointer
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How to prove this kind of statement: if $a$, then $b$ or $c$.

I think I saw a strategy to prove this statement is to suppose $a$ and $b$ are true then to prove that $c$ is false. Is it correct?
user546106
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Let ≤ be an ordering on a set A. Prove that if ≤ is a well-ordering then it is a linear-ordering.

So i understand that to be an ordering, you have to satisfy the conditions of being reflexive, anti-symmetric, and transitive and for linear-ordering , there should be any a,b such that a ≤ b or b ≤ a but I can't seem to find the connection unless…
matchesmalone
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Simple Absolute Value Proof

Let $\circ$ be an inequality. Prove $|x| \circ a \equiv -a \circ x \circ a$. If $x$ is positive, then $|x| \circ a = x \circ a$. If $x$ is negative, then $|x| \circ a = x \circ a$ ?
A_for_ Abacus
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Prove that if $r$ is a real number such that $|r-1|<1$, then $\frac4{r(4-r)}\ge1$

This was a bonus question on our last test. I'm not sure how begin. Would it be correct to say that since $|r-1|>0$, $0
user538039
  • 3
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Proving an equation holds for all integers

If I'm asked to prove that an equation holds for all integers, how should I go about it? My initial reaction would be to conduct two tests. The first one I plug in 2x into both sides of the equation and reduce and see if it comes out to the same…
JosephTLyons
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Prove the following equivalence (rationals)

I'm working on trying to prove the following equivalence for all x in real numbers: $x$ is rational $\leftrightarrow x - 5$ is rational $\leftrightarrow x/3$ is rational I know i need to prove each one individually such as: $$x\,\,is\,\,rational…
below_avg_st
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Is $f:\mathbb{R}^2 \rightarrow \mathbb{R}^2 ,f(x,y)=(x+4y,-3x-12y)$ surjective?

I am asked to determine if $f:\mathbb{R}^2 \rightarrow \mathbb{R}^2 ,f(x,y)=(x+4y,-3x-12y)$ is surjective, and provide a proof. I am having some trouble approaching this problem. Rewriting this as $x+4y=a$ and $-3x-12y=b$ shows that $0=-3a+b$ after…
Brandon O'Neil
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