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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Proof by Deduction $\sqrt{xy} ≤ \frac{x+y}{2}$

I want to ask a question about proof of deduction. I sat my Pure Mathematics Exam more than $3$ years ago but decided to return to the subject for a refresher. Proofs were not a requirement for my course but as my younger siblings are studying it,…
vik1245
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Proving that $\sqrt{\sqrt{\sqrt{\sqrt{\frac{1+\sqrt{5}}{2}+1}+1}+1}+1} = \phi$

I have this statement: Prove that $\sqrt{\sqrt{\sqrt{\sqrt{\frac{1+\sqrt{5}}{2}+1}+1}+1}+1} = \phi$ I have tried to develop algebraically, without having anything concrete. I have only obtained the longest problem, since I have tried to raise to 2…
ESCM
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How can I prove that $2a^2 + 2b^2 > ab$

I know that this statement is true, but I cannot figure out a way to actually prove it. $a$ and $b$ are both positive real numbers.
Victor H.
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Proof of an injection

How do I construct an injection from rational numbers $\mathbb{Q}$ to integers $\mathbb{Z}$? I need to write a proof and I'm not sure how to format it.
fadsfsa
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How to "prove" two objects are equivalent.

Given two sets of objects: $a = (x, y, z)$ where $x \in X$ and $y \in Q \cup R$ and $z \in P \cup T$ $b_1 = \{ x \mid x \in X \}$ and $b_2 = \{ y \mid y \in Q \cup R \}$ and $b_3 = \{ z \mid z \in P \cup T \}$ How to go about "proving" that they…
Lance
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How do I prove this function is not surjective?

\begin{align*} g: \mathbb{N} & \to \mathbb{Z} \\ g(n) &= \begin{cases} \frac{n+1}{2} & n \textrm{ is odd.}\\ -\frac{n}{2} & n \textrm{ is even.} \end{cases} \end{align*} Since $0\notin \mathbb{N}$, I think this function is…
Brandon O'Neil
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Is there an opposite of proof by contradiction?

Suppose I want to prove $a=b$. I start by assuming $a=b$. I simplify the expressions and arrive at something which is always true like $1=1$. Does this mean that the original statement is true?
Ryder Rude
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Method of Proof

Consider a theorem of the form: (Something) iff $\exists$ a continuous function $f: X \rightarrow Y$ s.t. (something about the function). I'm unsure how one would go about proving the $(\rightarrow)$ direction. So we suppose that (Something) is…
T. Fo
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How can I improve this proof?

I am trying to write a proof that $a \vert b$ if and only if $da \vert db$. This is what I have so far: $da \vert db$ if and only if $\lfloor db / da \rfloor = db / da$ $\frac{db}{da} = \frac{b}{a}$ and therefore $\lfloor b / a \rfloor = b /…
jsj
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Proving less or equal than (Hamming code triangle inequality)

I was given the problem to prove the triangle equality for Hamming Codes, i.e. $d(x,z) \leq d(x,y) + d(y,z)$ I could construct a proof that $d(x,z) = d(x,y) + d(y,z)$ quite simply. However I am wondering if it is necessary to also prove that…
Inazuma
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What's the proper way to talk about angles being periodic?

In the case of a sphere, the azimuth angle is $$2\pi$$ periodic in that if you add $$2\pi$$ to any azimuth angle you get the same direction. Similarly, the polar angle is $$\pi$$ periodic. In stating this we have to assume that the domain of the…
Ten Times
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Fermat's Little Theorem or Euler's Theorem First?

Just a quick question. Do you think it makes more sense to introduce Euler's Theorem and then prove Fermat's Little Theorem as a corollary or prove Fermat's Little Theorem and generalise to Euler's Theorem?
Tsing Shi Tao
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How to proof for all sets $A$ and $B$: if $A^{\complement} \subseteq B$ then $ B^{\complement} \subseteq A$

I think that there is a proof for this because we have an implication which we can translate to an or statement: $\left[\text{If } A^{\complement} \subseteq B\text{ then }B^{\complement} \subseteq A\right]\equiv \left[\neg(A^{\complement} …
lederhoser
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Is this proof style legitimate?

Normally for direct proof of equality we have the form: Prove $$a = b$$ Proof (Style): We start with $a$ (or $b$) and show through a sequence of logically connected steps that $a$ is $b$ (or the other way around). $_{_\square}$ But, since I'm…
Zduff
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How ot proof that of $1-1=0$ and $(-1)x = -x$ holds?

Is there any proof that $1-1=0$ and that $(-1)x=x$? These proofs should be created using only multiplication, addition and several basic rules like $a+x=0$, $a+0=a$, $1a=a$ etc.
Gillian
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