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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Questions about proving by cases for a biconditional

Let's say I have a predicate, $\forall x\in h(x) : f(x) \leftrightarrow h(x) \lor g(x)$ I understand that when Q $\implies$ P that we do cases and assume both h(x) and g(x) in each case, however when it is P $\implies$ Q I'm not sure if I should…
user322058
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Proofs that include long terms

While writing a proof that included expansion of $(\sqrt{n} + 1)^8$ in which I know the first term has to be $n^4$, is it acceptable to write something like $(n^4 +...... + 1)$ if the $n^4$ is the only thing I really need to move progress further in…
hello
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Proving a decreasing, convergent sequence.

Let $t_1=4$ and $t_{n+1}= \sqrt{3+2t_n}$. How do I prove that $3
Erik Jones
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Proving Inequality Statements From Proofs By Induction

Is it possible to prove $$1 + \frac{k}{2} + \frac{1}{2^{k+1}} \ge 1+ \frac{k+1}{2}\ \text{?}$$
user299071
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inclusion-exclusion principle proof (Without summations)

Suppose $\mathcal{A}$, $\mathcal{B}$, and $\mathcal{C}$ are sets with $\mathcal{A} \cap \mathcal{B} \cap \mathcal{C} = \emptyset$. Then $| \mathcal{A} \cup \mathcal{B} \cup \mathcal{C} |$ = $|\mathcal{A}|$ + $|\mathcal{B}|$ + $|\mathcal{C}|$ Prove…
user299071
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How to negate this statement for a proof by contradiction

I want to try and construct a proof by contradiction but am having a hard time negating this statement. The statement that I am working with is There are only a finite number of points accepted into the set and this finite sequence converges to…
RustyStatistician
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Question with proof by contradiction

Given a collection of numbers, one may wish to find the "closest pair": two numbers in the collection that are not the same, but whose difference is as small as possible. For instance, if we have values 4, 11, 6 and 13, then the closest pair is…
yociyoci
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Proof by Contradiction

Prove by Contradiction: Let $a,b,k$ be an element of $\Bbb Z$. If $a|k$ or $b|k$ then $(ab)|k$. How should I proceed? I have $a=\frac{k+s_1}{l}$, $b=\frac{k}{r}$ and $k=abp+s_2$ where $s_1,s_2,l,r,p$ are elements of an interger.
Natalie VelaCruz
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If $A\subseteq\mathbb{R}$ such that $0$ is a limit point of $A$, is $\{ka : k\in\mathbb{Z}, a\in{A}\}$ dense in $\mathbb{R}$?

Let $A\subseteq\mathbb{R}$ such that $0$ is a limit point of $A$. Is the set $ZA:=\{ka : k\in\mathbb{Z}, a\in{A}\}$ necessarily dense in $\mathbb{R}$? P.S. Please on my current stage of learning I wish to and need to learn writing down formal proofs…
TCHuang
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proofs involving the triangle inequality.

$$\forall a,b \in R (|a+b|=|a|+|b| \iff ab \ge 0)$$ I'm really stuck on where to even start with this. I'm assuming it has something do to with the triangle inequality, but don't know how to apply it. Here's what I can figure out anyhow. but if $ab…
Osuynonma
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Proving that $4000(1 - 0.95^n) $ is true for this situation

I can see why the following formula is correct, but I'm not sure how to set about proving it. A man needs to spread 4000kg of sand over his garden. He decides to spread 200kg every day, but after the first day he discovers that he can only spread…
Matt
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Any nonempty closed bounded set contains its LUB and GLB.

Although this seems intuitive, I don't quite see how to prove this. A set $A$ is closed provided if $a_n \in A$ with $a_n \to p$, then $p \in A$. Since $A$ is bounded, then any nonempty $a_n \in A$ is also bounded so it has an LUB and GLB. But how…
Mr Defect
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If $a,b> 0$, $a\neq b$, and $a + b = 2$ prove that $ab < 2$.

Let $a$ and $b$ be two positive real numbers such that $a \neq b$. Also, $a+b=2$. Now it is required to prove that $ab<2$. Thanks for any systematic and mathematical proof.
Soham
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Proving with division algorithm

$$ Let \ b \ be \ a \ natural \ number \ and \ q_1, \ q_2, \ r_1, \ r_2 \ integers \ with \ 0 \le r_1 \lt b \ and \ 0 \le r_2 \lt b \ such \ that \ q_1b + r_1 = q_2b + r_2 \ then \ q_1 = q_2 \ and \ r_1 = r_2 $$ I'm assuming the division…
dendritic
  • 315
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Let a and b be real numbers such that 0 < a < b. Prove $\frac{a+b}2 > \sqrt{ab} > \frac{2ab}{a + b}$

Let a and b be real numbers such that 0 < a < b. Prove $\frac{a+b}2 > \sqrt{ab} > \frac{2ab}{a + b}$ How can I prove this? Been working for hours and got nowhere. I see $\frac{a+b}{2}$ and $\frac{2ab}{a + b}$ are almost reciprocals. Is this…
Tom Stanton
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