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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How to explain why this injection does what we want (basic math)

Below is a generalization of a few theorems that I am trying to prove. I am trying to make the proofs as easy as possible to understand (for, say, a math undergrad). Setup. I have two sets $X$ and $Y$ whose members can be thought of as (atomic)…
Rachel
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Why Is This Squared Modulo Prime Number Equation True?

I recently was trying to figure out if there was an simple way to tell how many unique outcomes can be produced from the following equation: $k^2 \mod m$ where $m$ is some odd prime number and $k$ is some integer. After running a series of brute…
Nick Zuber
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What words do you use to describe a bad proof?

I was writing up a proof, but wasn't satisfied with what I was coming up with. The logic is there, but I wasn't able to express it clearly in math lingo. I was about to describe my work as "floozy" but then I looked up the definition and decided…
Stephanie
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How to prove: $\bigcap_{n=1}^{k}(n, \infty) \neq \emptyset$?

How to prove that for every natural number $k >= 1$, the following holds: $\bigcap_{n=1}^{k}(n, \infty) \neq \emptyset$ ? I know that for every $k$, all the intervals will have the intersection: $(k, \infty)$ But how do I write this as a proof?
Jane
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The Dynamics of Contrapositive Proofs

The Wikipedia Link for contrapositive proofs states that proving if p then q is the same as proving if not q then not p. I don't completely follow why. Is there any way to understand what's happening without involving logic tables ? If logic tables…
Inquest
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Is this a viable proof?

I need to show that if $3n-1$ is odd then $n$ must be even. I'm doing this in cases. For the first case I am saying: $$n = 2k \Rightarrow 3n-1 = 6k-1$$ Let $$j = 3k \Rightarrow (3n-1) = (6k-1) = (2j - 1)$$ therefore if $n$ is even then $3n-1$ is…
user3256725
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Proving with prime

Definition of prime is that a natural number $n > 1$ is prime if the only natural numbers $m$ with $m|n$ are $m = 1$ and $m = n$. I'm guessing this means that the prime numbers can only be divided between $1$ and the prime number itself. But how can…
dendritic
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Give a direct proof that, $n^3 > n^2 − 6n + 4$ for all $n ∈ {\mathbb N}$ with $n ≥ 2$ .

I have proved this by induction but with direct proof, I'm not really sure where to start. Thank you. Give a direct proof that, $n^3 > n^2 − 6n + 4$ for all $n ∈ {\mathbb N}$ with $n ≥ 2$ .
Danny Rancher
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Prove that $\exists z \in \mathbb R\forall x \in \mathbb R^+[\exists y \in \mathbb R(y-x=y/x) \iff x \neq z]$

This is Velleman's exercise 3.4.13: Prove that $\exists z \in \mathbb R\forall x \in \mathbb R^+[\exists y \in \mathbb R(y-x=y/x) \iff x \neq z]$. I am am stuck on that one. Seems like I am missing something. Besides I am having issues using the…
Eugene
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Greatest common divisors equal?

Let $a,b$ be natural numbers. Show that $gcd(a^n,b^n)$ = ($gcd(a,b)^n)$ for any integer $n$. How I started was first proof by contradiction, and then tried to do an inductive proof when that didn't work, but neither of them worked out for me. I…
Rdewolfe
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Injection proof

Prove that if f is injective, then $f(A \cap B) = f(A)\cap f(B)$ My answer: i) $f(A \cap B) \subset f(A) \cap f( B )$ Take an $x \in A \cap B$. $x \in A \cap B \implies x \in A \land x \in B$ $x \in A \implies f(x) \in f(A) $ $x \in B \implies f(x)…
Silva
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Josephine problem

So the problem is Suppose there are $2n$ people in a circle; the first $n$ are “good guys” and the last $n$ are “bad guys.” Show that there is always an integer $m$ (depending on $n$) such that, if we go around the circle executing every $m$th…
Garmagon117
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How do I write this proof formally?

How can I formally prove that $$\max\{\lvert x+y\rvert _i \} \leq \max\{ \lvert x_j \rvert \} + \max\{\lvert y_k \rvert \}$$ Where $x,y$ are the components of a $n$-vector with $1 \leq i,j,k \leq n$ It's obvious that if either $x$ or $y$ on the…
Christian
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Prove by contradiction that a circle chord is no longer than its diameter

Can anyone help me with this homework question of mine? I'm actually new to proofs. Here's the question, "Prove, by contradiction, that no chord of a circle is longer than a diameter." My only knowledge on proof by contradiction is on conditional…
k7dy
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Proving the recursive formula for "Virahanka Numbers"

So apparently Virahanka was an Indian mathematician that, in a way, discovered the Fibonacci sequence 500 years before Fibonacci. He was interested in finding the number of patterns of short syllables ($S$) and long syllables ($L$). We let $p$ be a…
user220329
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