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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Expressing variable in terms of other independent variables.

I am going through a proof for the existence of temperature (a proof written in C. J. Adkins equilibrium thermodynamics, if anyone is interested) and I am confused about one of the steps. I am hoping someone will be able to clarify it for me.…
Magpie
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Proof for converting powers into roots

What is a proof for the rule $$\sqrt[n]{a}=a^{\frac{1}{n}}$$ Is this just a definition or can it be proven? If just a definition, how come it just happens to match perfectly in the series of other types of…
Steeven
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Writing direct proofs

Let $x$, $y$ be elements of $\mathbb{Z}$. Prove if $17\mid(2x+3y)$ then $17\mid(9x+5y)$. Can someone give advice as to what method of proof should I use for this implication? Or simply what steps to take?
user58315
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Prove that $f(n) = n^2 - 1$ is not injective and not surjective. Am I doing it right?

Determine if $f(n) = n^2 - 1$ is injective, surjective, and prove your answer. The domain and codomain is the set of all integers: $\mathbb{Z}$ Let $-3 = n^2 - 1$ Then $n = \sqrt{-2} \notin \mathbb{Z}$ $\therefore f$ is not surjective. Let $f(n) =…
Leonardo
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Proof with inequalities

I have been assigned this problem for homework: Show that, if $a < b + \epsilon$ for every $\epsilon \gt 0$, then $a\le b$. I have tried to go about this using Induction, but I don't know what the base case would be. It is obvious to me in my…
Sam
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Personal experience in finding and writing proofs in general

Im curious to know if the art of writing proofs can be the same as finding a proof? Because to know wether there is a proof one has to be able to know how to write it. I like simple equations, because they are understandable for someone like myself,…
user366820
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Prove: If $X$ and $Y$ are infinite, then $X\cup Y$ is infinite.

Proof: Suppose $X$ and $Y$ are any infinite sets. Then $$ \exists f:X \rightarrow X \text{ such that}\; f \;\text{ is injective }\;\land\; f(X) \neq X,\;\;\text{and}$$ $$\exists g:Y \rightarrow Y \text{ such that}\;\; g \text{ is…
Bill
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What is the difference between prove, show and find?

I have been practicing for a proof test. The more I practice the more I see those three words: Proof, Show and Find. Is there a formal definition on what a question is asking for when each of these words is used?
Allan Lago
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Prove that every number divides itself.

I'm sure these proofs i'm doing are trivial to most of you, but I'm going to persist with these from this book because the aim is to improve the technique of proof writing and mathematical communication. I'm also finding out some properties of…
Bucephalus
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How do I check if there is a proof for a certain theorem?

Yesterday I proved my first theorem! It's quite dumb and all, but it says that for any number of sides n, the polygon with most area you can inscribe in a circumference is a regular polygon. I haven't found a proof for anything like this, but I'd…
ChemiCalChems
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What does "imply" mean in a statement?

Does imply means two directions are both true, i.e. "equivalent to," or just one direction, i.e. "shows?"
Vivian L.
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How to prove $a = c$ if $a = b$ and $b = c$?

It seems like a simple question, but is actually quite hard to prove. You don't just simply say: $a = c$ because $a = b$ and $b = c$. Like I actually want a proof behind it, something like using formulae, arithmetic, etc. How is this possible?
Zerium
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Solving inequalities by creating a function.

I have noticed a few answers involving inequalities proven by creating a function comprised of the terms in the inequality. I hadn't seen this before and was wanting to know more about how to use it. From what I have seen, it goes something like: I…
stariz77
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How to give an alternative proof of the chain rule using the little-o notation?

The chain rule. If $g$ is a function that is differentiable at $x$ and $f$ is a function that is differentiable at $g(x)$, then $f \circ g$ is differentiable at $x$, and $(f \circ g)'(x) = f'(g(x))g'(x).$ Question: I know the definition of the…
TCHuang
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Prove using PMI that if $A$ is denumerable and $B$ is finite, then $A \cup B$ is denumerable.

This is what I have thus far: Claim: If $A$ is denumerable and $B$ is finite, then $A \cup B$ is denumerable. Proof. Suppose $A$ is denumerable and $B$ has $n$ elements and $B = \{b_1, b_2, b_3, \ldots, b_n\}$. (i) Let $n = 1$. Then $A \cup B = A…
Amber Porter
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