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
-1
votes
1 answer

Proof that this set is convex set

I need a help with prooving that a given set is a convex set: $A \in \mathbb{R}^{m\times n}, c \in \mathbb{R}^n , b\in \mathbb{R}^m:$ $? \in argmin\{ c^Tx| Ax=b,x \geq 0\}$ I know the definition of convexity: $S \in \mathbb{R}^n$ is a convex set if…
user1762087
  • 103
-2
votes
1 answer

Is $\mathbb{R}\setminus\mathbb{Q}$ countable?

I need to prove that $\mathbb{R}\setminus\mathbb{Q}$ is countable or uncountable. I believe it is uncountable. I am not sure how to prove it. $\mathbb{R}$ is known to be uncountable and $\mathbb{Q}$ is countable. By reason when I take the difference…
user145469
  • 1
-2
votes
2 answers

Proving nice divisibility

Let $n=10x+y$ where $n$, $x$ and $y$ are positive integers. Prove that $n$ is divisible by $13$ iff $x+4y$ is divisible by $13$. I let $n=13k$, thereafter mutliplied $x+4y$ by $10$, to get $10x+40y$ and $n=10x+y$. Subtract the two to get $39y$ which…
Daiyuan Han
  • 5
  • 4
-2
votes
2 answers

How to prove that if $x>0$, $y>0$, and $x>y$, then $x^2>y^2$?

Prove that if $x>0$, $y>0$, and $x>y$, then $x^2>y^2$. Here is my attempt: Since $x>0$, $y>0$, and $x>y$, may implies that $x+y>0$ and $x-y>0$. Thus, $(x+y)(x-y)>0$. Simplifying this $x^2-y^2>0$ Therefore, $x^2>y^2$.
AYA
  • 578
-2
votes
2 answers

How would you do a proof of 'n' is the sum of two consecutive perfect squares, prove 2n-1 is a square number

'n' is the sum of two consecutive perfect squares, prove 2n-1 is a square number
otterandseals19
  • 15
-2
votes
3 answers

Prove that the set $X=\{1/n : n \in \mathbb{N}\}$ has no minimum.

I am not sure how to go about the proof. It makes sense that the sense has no minimum because each element in the set is becoming smaller and smaller than the one preceding it. However, I am not sure how to write it is as proof. I know I am supposed…
Hannah Diaz
  • 57
-2
votes
2 answers

Proving an Equation is False

When you have an equation such as 3271^11 + 5012^11 = 5193^11, what is the best way to prove it is false?
FΣynman
  • 1
-3
votes
2 answers

Prove using proof by contradiction

I was given the statement "for any integer n and prime number p, if n is divisible by p, then n+1 is not divisible by p" and I have to do proof by contradiction. Here's what I have so far... (Note: I don't know how to do the symbols on here so that…
Stephen R.
  • 1
-3
votes
1 answer

Choice of proof by contradiction

Why is it that whenever we wish to prove a negative claim that it is often a good approach to construct a proof by contrdiction
atifcppprogrammer
  • 5,852
-3
votes
2 answers

Is a proof by counterexample considered a proof by contradiction?

My question is already in the title. Let us look at some example. I would like to prove that a game $G(n,m,u)$ does not have a pure Nash equilibrium (PNE), for example. I did it like this: Suppose that the game $G(n,m,u)$ does admit at least one…
Learning
  • 105
  • 6
-4
votes
1 answer

How to prove if n>2 is a prime number, then n is odd?

I understand why this is true, but I have no idea on how I'd go about proving it by writing a detailed structured proof. Since a prime number is a integer, I started off like this: Assume n in Z Assume n > 2 and is a prime Then...? I…
muros
  • 417
-4
votes
2 answers

For all integers of n, $n$ is divisible by $2 \iff n^4$ is divisible by $2$

Provide the proof: $\forall n \in \mathbb{Z}$, $n$ is divisible by $2 > \iff n^4$ is divisible by $2$. Just curious on how the proof of this statement would look like.
Dike Doke
  • 1
1 2 3
…
50
51