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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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Proof by Contradiction: Opposite Angles of a Parallelogram

Prove the following statement by contradiction: "the opposite angles of a parallelogram are equal." Proofs by contradiction involving words like this are super confusing to me as I just generally don't know where to start? Obviously the very first…
plaguemasks
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Describing proof methods

My professor wants me to write the proof method of every proof at the beginning. Something of the form $\textbf{proof. }\textit{[proof method.]} \\ [\text{body}] \\ [\text{conclusion}] \\ \square$ What do I call my method if I use something like the…
Lex_i
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And integer proof question involving fractions

Sorry to ask two questions but I would ask: What conditions will these two fractions$$\frac {p^2+t^2} {p-t} $$ and $$\frac {pt(p+t)} {p-t}$$ Both be integers. I found that not all the time the fraction can both be function. Obviously $t=p-1$ will…
xxxx036
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Proving a statement: The set A={a,b,c} is a finite set with three elements.

It is from maths workshop course, we were asked to prove statement below. The set $A=\{a,b,c\}$ is a finite set containing three elements. I rewrote this as: Let A={a,b,c} be a set $\iff$ A is a finite set conaining three elements.$\qquad…
flowian
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Equivalent proof strategies

I am trying to prove that 4 statements, say A, B , C , and D are all equivalent. Would this string of implications get me to my desired results. I can prove that $A \iff B$, $A \implies C$ , $C \implies D$, and $D \implies A$. Am I missing an…
An Isomorphic Teen
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Proof of a result in $W^{1,p}$

I have to do this exercise: $\bullet$ Given $u \in W^{1,p}$ and $h=te_i$, $1\leq i\leq N$, prove that $D_hu$ converges to the $i$-th weak partial derivative of $u$, as $t\rightarrow 0$ in $L^p(\omega)$, $\omega \subset \subset \Omega$. I have no…
FRANCESCO
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How to present cases when writing a proof.

I was writing a proof where I wanted to show a statement y is true and ended up with two different cases to consider which were essentially: $x = 1$ and $x \neq 1$. I showed the result I wanted is true in both cases and I was just wondering how I…
Henry Brown
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Prove$ (2^n+3^n) ^{1/n}$ is a decreasing sequence

We want to prove this without using any calculus.
Aneesh Gupta
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Prove by induction that for any integer $n \geq 7, 3^n \leq n!$, where $n! = n(n-1)(n-2)...$

This is a practice problem, and but I am having trouble what I should do. I am new to proof writing, so I am a little bit uncomfortable with induction. Question: Prove by induction that for any integer $n \geq 7, 3^n \leq n!$, where $n! =…
maraik2002
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Showing the Proof

In upper level math courses it can be sort of relieving to see the word "show" as opposed to "prove" every once in a while. The difference has always been pretty clear to me, but I had a case where my professor did not share my understanding of the…
Algebraic
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Proof by contradiction question, falsum symbol used

I have a question on proof by contradiction. The Wiki page steps are to assume $\lnot P$ and derive a contradiction, formulated $\lnot p \implies \bot$. The law of non-contradiction is $\lnot(q \land \lnot q)$. Wiki explains $\bot$ is the logical…
Nick
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Proof by induction in sequences

My lecturer left this as an exercise and didn't go through it, I couldn't find it anywhere online so how is it done? Any help appreciated. Original question: "Let $(x_n)$ be a real sequence satisfying that every subsequence of $(x_n)$ does not…
Sam Connell
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Is this exercise on proofs mathematically correct?

I was doing some exercises on proof techniques from the book "Proofs and Fundamentals: A first course in abstract mathematics" and then I saw this exercise which is as far as I know incorrect. The exercise says: Let c be an integer. Suppose that c ≥…
brahWasHere
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Proof: For all real numbers $x$ and $y$, if $\lfloor 2x\rfloor = \lfloor 2y \rfloor$ then $\lfloor x\rfloor = \lfloor y \rfloor$

Here is what I have so far: The statement is true. Let $x$ and $y$ be real numbers and assume that $\lfloor 2x\rfloor = \lfloor 2y \rfloor=n$, where $n$ is an integer (we are trying to prove $\lfloor x\rfloor =\lfloor y\rfloor$). Then $n \le 2x < n…
user838441
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How do you prove $10^n + 3(4)^{n+2} + 5$ is divisible by 9?

I was able to do it making the $10^n$ substitution ($10^{k+1} = 10^k (10)$). However, I cant prove it making the $3(4)^{k+2}$ substitution. It should definitely be possible, but I am stuck at $10^{k+1} + 4(9J) - 4(10^k) - 15$ (where J is an…
user71207
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