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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Show that non zero vectors exist $\textbf{b}$ and $\delta \textbf{b}$ satisfying these functions.

Show that for non-singular $A \in R^{m\times m}$ there exists non-zero vectors $\textbf{b}$ and $\delta \textbf{b}$ in $R^m$ such that the following equations hold: $A \textbf{x} = \textbf{b}$, $A (\textbf{x} \delta \textbf{x}) = \textbf{b} +…
rioneye
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Prove that it will always be possible to find such two weights so the weight difference between them wouldn't be bigger than 1 kg.

You have 40 weights. It is known that the difference of weight in every 2 weights is no bigger than 45 kg. Also, it is known that you can divide every single group of 10 weights into 2 groups (5 weights in each) and the sum of weights in these 2…
thomas21
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Can I prove this statement like this?

The question asks $\forall x \in \Bbb R$, if $x > 3$ then $x^2 > 16$. The solutions tell me to find all intervals/cases for $x$ and prove that for one of the intervals, the hypothesis $x > 3$ is true and the conclusion $x^2 > 16$ is false, and if…
ming
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How to prove an implication within an if and only if

Suppose you need to prove that $A\iff (B\implies C)$. The two ways to prove this are: (1a): Suppose $A$ and $B$ are true. Prove that $C$ is true. (1b): Suppose $B$ and $C$ are true. Prove that $A$ is true. (2a): Suppose $A$ and $B$ are true. Prove…
Marc
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Need help proving there is not a surjective function from A to the set of all functions from A to A

We have $F_A = \{ f|f:A\rightarrow A \}$ is the set of all functions from A to A, where A is a nonempty set that could be infinite. I'm trying to show that if $|A|>1$ then $|A| < | F_A |$. I have shown that $|A| \leq | F_A |$ by finding a one to one…
J. Rowe
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How to prove that $n^{\frac{1}{3}}$ is not a polynomial?

I'm reading Barbeau's Polynomials, there's an exercise: How to prove that $n^{\frac{1}{3}}$ is not a polynomial? I've made this question and with the first answer as an example, I guess I should assume…
Red Banana
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Ending a proof with "the result follows".

Let's say I was writing a proof that required a lot of leg work or "rough work" in order to arrive at the conclusion. I want to show the reader (say a professor) that rough work because it's important. The actual proof after the work is trivial but…
Zduff
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Prove that $2^n>\frac{n(n-1)(n-2)}6$ for $n\in\Bbb N$

Apparently, I'm supposed to prove this using the binomial theorem, but that doesn't seem intuitive. Can't I just say Prove that $\exists n\in\Bbb N$ such that $$2^n\le\frac{n(n-1)(n-2)}6$$ And show that $n=1$ contradicts this? Is that a valid…
Anthony P
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Uniqueness Proof procedure

I'm reading a book on understanding math proofs to enable me to understand mathematics at a deeper level. Along the way I came across this: An element belonging to some prescribed set $A$ and possessing a certain property $P$ is unique if it is…
John
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When should I use "let" "put" "be" in a proof?

From reading some instructions I could find online, I could understand that this isn't universally agreed upon, but in a course I'm taking now the professor insists on a particular connection between the proposition one needs to prove and stating…
wvxvw
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Assuming a Solution Exists

Students who are beginning to learn proofs (and some seasoned pros) occasionally commit the error of assuming what they're trying to prove. My question involves assuming at the onset that a solution to a problem exists, then using that existence to…
Jon
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Another proof question for real analysis

Let $a, b, c \in \mathbb{R}$. Prove if $a + b = a$ then $b = 0$. Suppose that $a + b = a$. Then $a + b - a = a - a = 0 = b$ by the inverses law for addition. By the Identity law for addition it follows that $a + 0 = a$, and it follows by the…
middleRingRider
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How do I make this simple proof better (and more correct?)

Let $x$ and $y$ be real numbers. If $x\cdot{y}>\frac{1}{2}$, then $x^2+y^2>1$. Proof: We will prove with the direct method. Let $x$ and $y$ be real numbers. Since $$ x\cdot{y}>\frac{1}{2} $$ it follows that $$ 2xy>1,$$ which means $$x^2+y^2 \geq…
bjd2385
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How to learn developing the formal proof of statements or theorems?

This is not a math problem, but something that this platform can provide answers to. I am a student of math. I learn and understand the concepts. However, when I see some statements I understand how they're true, but when somebody asks me to prove…
CodeLover
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Proof About Point and Triangles

Suppose we are given $n$ points in a plane, where $n\ge 4$ and no 3 of the points are collinear. If $k$ distinct triangles are designated with vertices among the $n$ points, show that no more than $k(n-3)$ of the $n\choose 4$ groups of four points…
miamiheatftw
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