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 for two positive arrays with equal means and equal numbers of elements, the wider the distribution, the greater the cubic sum.

Known conditions: Two sets of positive number arrays A and B have the same average: (a(1) + a(2) + ... + a(N)) / N = (b(1) + b(2) + ... + b(N)) / N The minimum value in array A is less than the minimum value in array B: min(A) < min(B) The maximum…
XIAO LIU
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How do I read this question?

Here is the question I am dealing with: Disprove the statement: Let $f$ be a real-valued function with domain $(-∞,∞).$ Then $∀x,y {∈} (-∞,∞), \,f(x) = f(y)$ implies that $x = y.$ I am not looking for an answer to this problem, but I'm stuck on…
Olivia
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Prove that $x^3 = x^2$ has exactly two solutions

I saw someone proving the uniqueness like this: Suppose for a value $x=z$ such that $z\neq 0$ and $z\neq 1$, and $x^3=x^2$. Thus $z^3=z^2$. Since $z\neq 0$, multiplying both sides by $1/z^2$, we get $z=1$. Thus it contradicts with the assumption…
enoopreuse22
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Must the $\forall$ statement be used in front of the consequent statement?

Must the $\forall$ statement be used in front of the consequent statement? For example, must we write $\forall x\in\mathbb{Z}^{+}, x>0$, or can we also write $x>0, \forall x\in\mathbb{Z}^{+}$ In proofs, the 1st one is most common, but I have a…
IraeVid
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Question about how to prove a inequality

I am self learning math proofs and I'm just having trouble understanding something. Say that I was to prove that any positive function is greater than $0$. Take the random example $x^2 +5x+ 7 > 0$ for all real numbers x or smt. I don't know how the…
Learningmath
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Proof of the existence of a vector satisfying an equation

I need to prove or disprove there exists $\left(k_1, k_2, k_3, k_4\right) \in \mathbb{R}^4$ such that the following equation holds only if $\left(m_1, m_2\right)=\left(t_1, t_2\right)$ (where $t_1, t_2$ are two fixed numbers both from…
Aaron Zheng
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Elementary proof for $-v \leq u \leq v$ iif $|u| \leq v$

I'm having difficulties with writing proofs, probably because I've just started the subject. And i really would like to avoid looking at the answers and solve it as best as I can myself. Now I'm asked to give a proof of: $-v \leq u \leq v$ iif $|u|…
Apeiron
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Elevator Disposition Proof of Impossibility

Let the highest floor of a building be an integer L. There are 2 elevators A and B, where A starts at floor zero and B starts at floor L. If someone presses the elevator button on floor N, the closest lift to that floor N will move to that floor.…
SeeMore
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What is a self-contained proof?

For this question I am required to give a self-contained proof of a statement, but I am not sure what a "self-contained proof" is.
nonion
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Is $\square$ an alias for QED?

In math, proofs are often accompanied by 'QED' (quod erat demonstrandum) at the end, indicating their conclusion. Some authors use a square symbol ($\square$) instead of QED, with the same meaning. Can we say $\square$ is an alias for QED? If not,…
sam wolfe
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Let $\,u,v,x,y\,$ be real numbers. Prove that $ux+vy\leqslant\sqrt{u^2+v^2}\!\cdot\!\sqrt{x^2+y^2}$

I am unsure how to go about this. This is a question for a mathematical proofs class at my University and the only proofs we have been exposed to so far are direct, contrapositive, and contradictory proofs. I tried squaring both sides but that…
Tom Brady
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How to Prove paths in a grid formula by Proof by Induction?

I was recently watching a video on Khan academy, https://www.khanacademy.org/math/math-for-fun-and-glory/puzzles/brain-teasers/v/path-counting-brain-teaser where he works through a problem about finding all possible paths in an n X n grid from the…
Dadaloglu
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multiplication of two consecutive numbers

a, Is it true, that if $n \gt 1$ odd number, then we can express ${n^2-1\over 4}$ as multiply of two consecutive numbers? b, Is it true, that we can express ${n^4+2n^3+3n^2+2n\over 4}$ in case of n= all natural numbers, as multiply of two…
Holdviola
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Prove $a^{1/k}+b^{1/k}\gt (a+b)^{1/k}$

Prove the statement(#): (#) Suppose $k$ is an integer greater than $1$. Suppose $a,b$ are positive real numbers. Then $a^{1/k}+b^{1/k}\gt (a+b)^{1/k}$. How should I start the proof? Any inequalities I can apply? Which topic is related to this proof?…
sunny
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First proof writing practice: writing and style feedback, and is it correct?

I'm not even sure if this is correct because there was no answer in the book and I'm new to proofs by induction. I'm mostly interested in feedback about the style and any proof-writing faux-pas'sss I may have made. It felt right to put the lemma up…
user2170751
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