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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How do I prove that a BBP type formula is true?

I have come across a general BBP type formula to calculate the natural log of any integer greater than one. How do I prove that it is true? $$\ln(n) = \sum_{k=1}^\infty \left( n^{-k} \cdot\frac{(n-1)^k}{k} \right) \text{when } n \gt 0$$ The…
JacobTDC
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How to transform a truth table into a proof?

So here is my problem, I am asked to prove that P $\leftrightarrow$ (Q $\leftrightarrow$ R) is equal to (P $\leftrightarrow$ Q) $\leftrightarrow$ R, pretty straight forward. So I made this truth table to prove it, and the truth values match up…
fsdff
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Proving equality of sets for a in the reals

I am trying to prove that the sets A={functions of the form $x\rightarrow16^{ax}$} B={functions of the form $x\rightarrow2^{ax}$} for a in the rational numbers are equal. I know that I must prove that A is a subset of B and that B is a subset of…
Isa.S
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Proof Writing for Abbott Exercise

I've just picked up Abbott's analysis book, and I am faced with the following problem. While it's quite simple, I am not very familiar with formal proof writing, which is what I am finding difficult. The problem is the following: Prove or…
高田航
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The method of contradiction?

Are there any basic rules and crucial things to be known about employing the method of contradiction to prove anything?
user516517
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Proof that $+0=-0$ by using only: *the definition of 0 *The associative law *The commutative law

I know the question has already been asked here but both answers it got used something they call "the transitive property of inequality" and "the subtractive property of inequality". I got this task from Chrystal's Algebra: An Elementary Textbook…
Felmola
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if $n$ is an element of $\mathbb{Z}$, then $\gcd(n,n+2)$ is an element of $\{1,2\}$.

I've gone with the approach of letting $n$ be either even or odd. I was able to solve for the case when $n$ is even but i don't know how to approach the case were $n$ is odd. I've done the scratch work but I don't know how to word it or how to make…
P.Sanchez
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Mathematical Strong Induction Proof involving recurrence

I'm quite comfortable when it comes to simple induction. However, whenever I encounter a strong induction problem, I don't know how to approach it... Thank you for contributing. http://puu.sh/yfFlI/be31254ac6.png $\forall n \in N^+, t_n < 2^n$
user498021
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Strong Mathematical Induction

$ a_n=\left\{ \begin{array}{ll} 2 & n=1 \\ 6 & n=2 \\ a_{n-1}+9a_{n-2} & n\geq 3 \\ \end{array} \right. $ $\forall n \in N^+$, $a_n < 3^n$. So far, I have assumed that $a_{n-1} \le (n-1)$ then, $(n-1) + 9(n-2) < 3^n$, then $10n-19 < 3^n$. Does…
user498021
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Stuck creating proof

I am having trouble working about a proof for the claim: If a and b are any rational numbers, with b not equal to 0, and r is any irrational number, then a+br is irrational. This is all I really have so far... Proof: Let rational numbers a and b as…
user497853
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Each composite (positive) $n$ has a (positive) prime divisor no greater than $\sqrt{n}$.

$\forall n \in \mathbb N^+$, $n$ is composite $\;\rightarrow\; \exists p\in \mathbb N^+, p \textrm{ is prime and } p \leq \sqrt{n} \textrm{ and } p\; |\; n$. So far this is what I have... Suppose this is false. $p> \sqrt{n}$, $p|n$ Then, $p^2 >…
user496555
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Proofs in discrete mathematics

$\forall n \in \mathbb{N}^+, r\in \mathbb{N}^+, s\in \mathbb{N}^+, r\cdot s \leq n \implies r \leq \sqrt{n} $ or $s \leq \sqrt{n}$ Assuming that $\mathbb{N}^+$ refers to all positive natural numbers starting at $1$. Can someone pls give me a hint…
user496555
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Manner of existential proofs.

Is this possible? Given that a set $A$ of infinite cardinality must have property $p$... To prove that a infinite set $A$ cannot exist if it is to have property $p$, we can start from one arbitrary element in $A$ and whilst constructing $A$ while…
Stone
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Prove that for all whole numbers $x, y, z$, there exists $\big(\frac{d}{2b} + 1\big)^2$ solutions for $x + by + cz = d$.

Prove that: $$\forall \{x, y, z\} \subset \mathbb{W}, \ \exists \bigg(\frac{d}{2b} + 1\bigg)^2 \text{ solutions for } x + by + cz = \left\{d : \frac{d}{2b} \in \mathbb{Z}\right\}$$ $\mathbb{W}$ denotes the set of whole numbers, which is the set…
Mr Pie
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Poorly Worded Math Problem - Buy Out Clause

I know the title isn't specific, but I read this clause. I have two people who read the math in two different ways. With all your math skills, how would you do the math on this clause? "Two times the sum of (i) that Member's ownership interest…
F. Miller
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