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 disprove a theorem

I have a question that says, Explain how to disprove a theorem of the logical form "$\forall x \in A, P(x)$". Write the logical form of the statement you want to prove. So disprove a theorem, wouldn't you just find a counterexample because it…
user6259845
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Trying to Understand How to write Proofs

I am trying to study for a proofs final, and I'm really struggling with writing proofs. Does anyone have any suggestions that might help me to write proofs when given a theorem? I know there are different strategies that can help you like if your…
user6259845
  • 913
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Prove (or check) the expression is positive given constraints on variables?

The following proof problem have taken me a few days. Perhaps it is too hard for me to overcome it. Can you help me? The expression is by the following: \begin{equation} \begin{split} &2\,x{c}^{x-1}\ln \left( c \right) -{2}^{x}\ln \left( 2 \right)…
FlyFish
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Inductive proof structure

To prove a statement about recursive series, is it correct to use an inductive proof structure showing that if $n = k$ and $n = k + 1$ are true then $n = k + 2$ holds true, and then prove the statement for $n = 1$, $2$ base cases?
Afiq Hatta
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How to prove that $\limsup X_n \leq \sup\{X_n\}$?

How to prove that $\;\limsup\limits_{n\to\infty}X_n \leq \sup\limits_{n\in\mathbb{N}}\{X_n\}\;$? I need to prove this and I don't know how to go about doing this. Thank you for any help you can provide.
Matt
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Is it necessary to prove equality from both sides?

I have asked this question yesterday, and my friend told me, to rememeber to "prove it" also from the other side e.g. Let x $\in$ Conv($M+u$).....then $x$ $\in$ Conv($M$)+ $u$. Why would somebody care for proving it from the other side, when using…
Martin
  • 155
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Logarithm proof by contradiction

Prove by contradiction that $\log_5 8$ is irrational. While I understand that this is true, I am struggling to prove it by contradiction. Thank you for any help!
Pamela Graham
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Proving by arriving to truth from an assumption.

It's easier to explain the question on an example. Let's consider this pretty simple problem: We have to prove that $(-1)a=-a$ where $a \in R $. My question is, can I prove this in the following way? $$(-1)a\stackrel{?}{=}-a \Rightarrow…
khajvah
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The relation between formal logic and proof writing

I was reading vellmans how to prove it and he forms a link between formal logic and proof writing. For instance, he decomposes if p then q to not(p and not q) and similarly for other such proof writing statements. However what I don't follow is…
Inquest
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Details of proof by contradiction

I realize this is pretty basic but recently became unsure of how to justify proof by contradiction. Is it that case that I can show $A\Rightarrow B$ by assuming $A$ and NOT $B$, and showing this leads to a contradiction? How can this be…
manofbear
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Prove that $3$ divides $n^2 + n$ iff $n$ mod $3$ $\neq 1$

I'm trying to prove that $3$ divides $n^2 + n$ iff $n$ mod $3$ $\neq 1$ . I already tried it with proving a double implication, but I did not succeed. A tip or kickstart would be great. Thank you
CPUFry
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If$(10000x^{2015} - x)\over (x^2+x+1)$is odd, then $4x^2 + 3x + 1$ is even.

How would I I begin to prove this implication? Starting with the hypothesis $(10000x^{2015} - x)\over(x^2+x+1)$ = $2(k)+1$. I'm sort of lost on where to go?
Christopher
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Induction Proof with Fibonacci

How do I prove this? For the Fibonacci numbers defined by $f_1=1$, $f_2=1$, and $f_n = f_{n-1} + f_{n-2}$ for $n ≥ 3$, prove that $f^2_{n+1} - f_{n+1}f_n - f^2_n = (-1)^n$ for all $n≥ 1$.
Eugene Wales
  • 39
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Prove this theorem: If the product of two consecutive integers is not divisible by 6, then it can be written in the form 9t+2 where t is an integer.

I know that product of two consecutive integers must be even, but not too sure how it helps in proving this.
yociyoci
  • 69
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proving a hard inequality

can someone help me to prove this inequality : $\left| \sum _{ k=0 }^{ 2n }{ \frac { k }{ k+{ n }^{ 2 } } } -\sum _{ k=0 }^{ 2n }{ \frac { k }{ { n }^{ 2 } } } \right| \le \frac { 4 }{ { n }^{ 2 } } (2n+1)$
Khalil Hafni
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