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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The closure of $S$ is the set of all limits of sequences of points in $S$ that converge in $E$

My book asks the reader to prove that the closure of $S$ (the intersection of all closed sets in $E$ that contain $S$) is the set of all limits of sequences of points in $S$ that converge in a metric space $E$. I believe I have a proof for this but…
Christian Chapman
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Proofs in Discrete Math

∀n∈N+, n composite → ∃p∈N+, p is prime and p≤√n and p|n Am I supposed to prove that p≤√n and p|n when n is composite and p is prime? Could someone fix my translation if I'm wrong? Thanks!
user496555
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proving f(n) is strictly less than 2.4 when $n\geq 1$

$f(1)= 2, f(n+1) = \sqrt{3+f(n)}$. Prove $f(n) < 2.4$ for all $n ≥ 1$. Would this be a proof by induction? If so, could somebody start me off?
Seth Killian
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what is the necessary proof that should be handled as a student major in math?

I am a student in community college and I plan to transfer to uc in my third year but our college don't teach us proof so I want to know what proofs are necessary to handle when in my first and second years. looking forward to your help!!
user450666
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prove that $a\mid b$ is not a partial order

prove that $a\mid b$ is not a partial order on integers $\mathbb{Z}$ I'm really lost how should I prove that?
Jack F
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Solving for y in the equation $y^x$ = $x^y$

Once upon a time as a high school freshman I stumped all the math teachers and tutors by asking them to solve for y in the in the equation $y^x = x^y$. I asked Wolfram alpha to solve for y and it returns $$y =…
Ryan
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How to prove that O is the centre of the circle??

In the image,It is given that OA=OB and angle(AOB)=2*angle(ACB). Then,prove that O is the centre of the circle. I need some hint for solving it.Please help.
CandidFlakes
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Prove that $\sin (n\beta)$ can get arbitrarily close to any value in [0, 1] if $\frac{\beta}{\pi}$ is irrational

I saw the following statement and I'm not sure how to prove it: Given a constant value $\beta \in \mathbb{R}$, if $\frac{\beta}{\pi}$ is irrational, then for some value $\alpha \in [0, 1]$, $\forall\epsilon \in \mathbb{R}:\epsilon > 0$, $\exists n…
Sully Chen
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Wording: A is bounded above by B, independent of C

Is the sentence A is bounded above by B, independent of C. correct? I am not sure whether it should be independently instead of independent. I am sorry for asking this here instead of ell.stackexchange.com, but in my experience I get more…
Bananach
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"...everything that you are assuming to be true is the hypothesis.". Is this true? Reasoning about proofs.

I am trying to improve my ability to reason about proofs. To accomplish this, I am studying the textbook, "How to read and do proofs", by Daniel Solow. In the textbook, Solow makes the claim that "...everything that you are assuming to be true is…
The Pointer
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Need some help with an even/odd proof by contraposition.

Let me preface this by saying I am horrible at math, and I apologize for the dumb question. So, I'm trying to prove that "for all integers , if (^2) + 2 is even, then is even.", and it has to be by contraposition. This is what I have so far: By…
davidib17
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Proving that $f(x)= \frac {(x+1)}{(x-1)}$ is onto

How would I go about proving that the function is onto for: $f(x)= \frac {(x+1)}{(x-1)}$ if x does not equal to 1. And $f(x)=1$ if $x = 1$
Jake0991
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Verification if a>b>0 then cube root of a is bigger than cube root of b

I am trying to do this proof. Please tell me if it is correct. Please help me also with the mathematical symbols. If a>b>0 then cube root of a is bigger than cube root of a. Case 1: Suppose for the search of contradiction that cube root of b is…
Beginner
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Let $n$ be a positive integer Prove that if $\sqrt {n}$ is a rational number then it is actually an integer.

Actually, it is obvious. But, I could not prove. Can you hint?
user295645
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Looking for a 'quick-and-dirty' resource for proof techniques

I have limited time to spend on the resource (3-6 hours) and never done any proofs and I need to be able to apply deductive, inductive and other proof techniques to some relatively easy propositions (basic number theory, trees etc.). Please…
Wuschelbeutel Kartoffelhuhn
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