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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Propositional Logic help

Trying to get a transformational proof for "$(-p\vee q) \wedge (-q\vee p)$" to "$(p\vee q) \to (p\wedge q)$", any idea on the next step I can take? I'm not looking for an answer just a hint. Thanks
Aaron Patterson
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If a and b are integers with $a < b$, then the average of a and b is greater than a and less than b

I need a direct proof for "If a and b are integers with $a < b$, then the average of a and b is greater than a and less than b." I have so far: Hypothesis: A and B are integers and $A < B$ Conclusion: $ A < \frac{A + B}{2} < B $ But I'm not really…
GiantDuck
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Proving Inequality relation on integer set.

Let $a,b\in \mathbb{Z}$, Suppose $a
Alex
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Suppose $n^2 + 1$ is a prime number. Then $n + 1$ is also a prime number.

Since this proposition is false, I tried to do a counter-example. Is this a correct format of a counterexample for such proposition? Take $n = 3$, $3^2 + 1 = 10$, $10$ is not a prime number as it has factors of $1, 2, 5, 10$. $3 + 1 = 4$, $4$ is…
User426190
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Uniform continuity for a sequence of functions, $f_n (x)=x^n (1−x)$

I'm trying to prove the following. Prove $f_n :[0,1] \rightarrow \Bbb R$ defined by $f_n (x)=x^n (1−x)$ converges uniformly to zero. I know that for uniform continuity, we must find an $\varepsilon$ such that $|f_n(x)-0|
NoVa
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Big Omega Proof

If $f_1(x)$ and $f_2(x)$ are functions from the set of positive integers to the set of positive real numbers and $f_1(x)$ and $f_2(x)$ are both $\Omega(g(x))$, is $(f_1 − f_2)(x)$ also $\Omega(g(x))$? How do I prove/disprove this?
moo
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Prove that $n<2^n$ for any natural number $n$.

How do I prove that $n<2^n$ for any natural number $n$, assuming basic facts about the algebra of exponents?
3.14Pie
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Should one always place the proof of a theorem after its statement?

I'm writing up my solutions to a rather large set of number theory problems, and was wondering the following. I'm certainly used to writing formal, 'structured' mathematics solutions, but in these problems I've frequently found I want to split my…
damfal03
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Positive and Negative Real numbers

I stumbled upon this question on Yahoo answers here : Prove that for every positive real number x, l/x is also a positive real number.? Answering to the question is [now] closed, but I was thinking about the answer, when I sketched this argument…
JWL
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Let $x\in\mathbb{R}$ and assume that for all $\epsilon > 0$, $|x|< \epsilon$. Prove that $x = 0$. Use a proof by contradiction.

I appreciate any help you can give me in solving this problem.
Deryn21
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Are there other ways to prove this?

If $\frac{b+c-a}{y+z-x} = \frac{c+a-b}{z+x-y} = \frac{a+b-c}{x+y-z}$, prove that each ratio is equal to $\frac{a}{x} = \frac{b}{y} = \frac{c}{z}$. My attempt: By addendo, $\frac{b+c-a}{y+z-x} = \frac{c+a-b}{z+x-y} = \frac{a+b-c}{x+y-z} =…
MrAP
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Can I use this as a proof?

Some days ago, I've made this question and I guess I've finally found an answer to this question: (a) Is it possible to find a polynomial, apart from the constant $0$ itself, which is identically equal to $0$ (i.e. a polynomial $P(t)$ with some…
Red Banana
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Proof writing, iniqualities

I have been through a couple of proofs by now. I wonder why mathematicians need to prove something to be equal, by proving it can be higher or equal and less or equal. What is the point? They make use of epsilon all the time for that purpose. I…
Pedro Gomes
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Thm: If W is a subspace of a vector space V, then span(w) is contained in W. Is this proof valid?

Thm: If W is a subspace of a vector space V, and w1,w2,...,wn ∈ W, and a1,a2,...,an ∈ F (Field), then a1w1,a2w2,...,anwn ∈ W. Comment: I believe this translates to the title "If W is a subspace of a vector space V, then span(w) is contained in W."…
IgnorantCuriosity
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Prove or disprove: $\exists N_0 \in \mathbb N s.t. \forall n \geq N_0, 2^n > n^2$

This statement is true, for any $N_0 \geq 5$. My question lies in how to formally prove this. My professor is very strict about proof structure. This week, the homework mainly had to do with mathematical induction. Can this be proven using…
mh234
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