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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I don't understand part of a proof

I was reading a proof in my textbook today and couldn't figure out why this is true: $$ nq - mp = nq -mq +mq - mp$$ Any help would be appreciated.
user3182252
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Injection proof

Prove that for any $A, B \subseteq X$ we have $f(A \cap B) = f(A) \cap f(B)$, then $f$ is an injection. I get stuck at the step where $f(w) = y = f(z)$, since I am trying to prove it is injective, I can't just say they're equal right?
user127778
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Struggling with a proof that $-m=(-1)m$

Prove that For all integers $m$, $-m=(-1)m$. Any help would be greatly appreciated.
user127835
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Discrete Structures proof

I'm in a discrete structures class and I'm having trouble with formulating ideas as to what I need to prove. Here's the question: Suppose you are trying to prove that, If a, b, and c are integers for which a divides b and b divides c, then a divides…
Mdjon26
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Prove $\liminf(a_n) = \limsup(a_n) = \infty$

If $(a_n)$ is a sequence of real numbers, prove $(a_n)$ diverges to infinity iff $\liminf(a_n)=\limsup(a_n)= \infty$. I started with this but don't know if it is right or where to go next.... For $E>0$ there exists $N$ in natural numbers such that…
Jenna
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Why does $2^{-n} = 5^n \times 10^{-n}$?

If we look at the decimal equivilents of $2^{-n}$, we see they resemble $5^n$ with a decimal point in front of them: $\begin{align} 2^{-1} &= 0.5 \\ 2^{-2} &= 0.25 \\ 2^{-3} &= 0.125 \\ 2^{-4} &= 0.0625 \\ 2^{-5} &= 0.03125 \\ ... \end{align}$ It…
Cole Tobin
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EDIT: Proving $f^{-1}(f(C))=C$

I need to prove that $f^{-1}(f(C))=C$. This are the informations. There exists two sets A and B, and function $f(A)\to B$. I don't know how to solve this, and I tried to search google, but I didn't find anything useful. Please help. Thanks!! EDIT:…
depecheSoul
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Simple Proof question

Image : http://postimg.org/image/dkn0d5uen/ I'm studying Spivak's calculus and I have a really simple question : I'm only in the first chapter on "The basic properties of numbers" So far, we have the following propostion P1 : (a+b)+c=a+(b+c) P2 :…
user108343
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Cantor-Schroder-Bernstein Contradiction

I need help figuring out where to start a proof that says I should use a proof by contradiction. $f\colon A\to B$ and $g\colon B\to A$ be functions and each is 1-1. Let $D$ be the range of $f$ (i.e., $D=f(A)$). Let $x$ and $y$ be natural numbers…
Alex
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Prove that $S = \left \{(x, y) \in \mathbb{N} \times \mathbb{R}: xy = 1 \right\}$ is denumerable

In the solutions, the proof begins by defining the function $f : S \rightarrow \mathbb{N}$ by $f(x,y)=x$ and goes on to show that $f$ is a one to one correspondence from $\mathbb{N}$ to $S$. However, I don't really understand why the solutions chose…
Adrian
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Logic Proof: Help Starting out

I am having some trouble starting off this proof. I am not sure if I need to prove by the contrapositive or if it is a direct proof. Prove: If $x, y,$ and $z$ are natural numbers such that $x^2+y^2=z^2$ and $gcd(x,y,z)=1$*, then exactly one of the…
user111702
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Show that if x divides a power of 2, then x is a power of 2

I'm trying to prove that if $x$ divides $2^a$ for some integer $a \geq 0$, then $x = 2^b$, where $a \geq b$. In other words, if $x$ divides a power of 2, then $x$ is a power of 2. This makes sense, since the all the factors of a power of 2 are also…
devin64
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The 2 Ways to Prove Uniqueness - Interchangeable or Nonidentical?

Source: Mathematical Proofs, 2nd ed. by Chartrand. p. 121. An element belonging to some prescribed set $A$ and possessing a certain property $P$ is unique if it is the only element of $A$ having property $P$. Typically, to prove that only one…
user53259
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How do I approach this two column geometry proof?

I'm taking an online course and I'm a bit confused on what I'm supposed to do. I'm not looking for someone to do my school work for me, but if someone can explain to me how I should be approaching the problem would be great. Thanks. edit (response…
Ravenous
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Prove $\forall x, y \in \mathbb{N}$ there does not exist $x, y$ s.t $y^ 2 = x^2 + 2xy$ **without** using $\sqrt{2}$

Prove ${\forall x, y \in \mathbb{N}}$ there does not exist $x, y$ s.t. $y^ 2 = x^2 + 2 x y$ without using $\sqrt{2}$. Proving the statement with $\sqrt{2}$ is just a matter of taking the square-root of both sides: $$\Longrightarrow y^2 = x^2 +…
MaximeJaccon
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