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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To show that $A = B$, do I have to only work with one side of the equation and show that it equals the other side, without using the other side?

I need to show that A = B. Do I have to only work with one side of the equation and show that it equals the other side without using the other side? Or can I assume that they equal each other and use both sides together to show equality? For…
Nate
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prove that a sequence that tends to a limit, multiplied by n, the sequence will be kl.

Prove that if a sequence $s_n$ goes to a limit L as $n \rightarrow \infty $, then for a number $k > 0 $ then the sequence ${kn}$ will tend to the limi $kl$. Is this simply because k is isolated from the limit, meaning that k has nothing to do with…
user1090614
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Prove that any odd number can be expressed as $4n+1$ or $4n+3$

Prove that any odd number can be expressed as $$4n+1$$ or $$4n+3$$ I can see that this is true, but I am not certain on how to make a formal proof.
user1090614
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Prove that $3n +5m = 12$ for any two natural numbers.

Prove that $\exists n,m \in \mathbb{N}$ such that $$3n+5m=12 $$ This is clearly false, but I am not sure how to conduct a proof stating it is false. Should I just give examples with $n = 1,2,3$ and then pick $m$s afterwards?
user1090614
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Theorem proof of this equation

How would you prove the theorem $(-a)\cdot (-x)=ax$? If you used multiplication and addition axioms.
user103748
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professionally writing proofs

I am writing a proof for the Theorem (x-a)(x+a)=x^2-a^2 and directly proved it by manipulating the equation using multiplication and addition axioms. But I'm not sure what should be included in the intro and conclusion.
user103748
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Statement of a lemma

Suppose $\alpha$ and $\beta$ are sets. Suppose that the formula $\alpha\supseteq\beta$ is almost obvious. Now which of the following (true) alternatives make a statement of a lemma (used by one theorem…
porton
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Using a direct proof, how should I approach this question?

For integers $x$ and $y$, if $xy$ is even, then either $x$ or $y$ must be even. I know how to solve this in both a contradictive and contrapositive manner but can not quite figure out how to solve it with a direct proof. An identical problem was…
Arcangel0723
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proof by contrapositive method

$∀ ∈ ℕ, m^2 + 3$ is even ⟶ $m$ is odd $P = m^2 + 3$ is even $Q = m$ is odd By contrapositive: $¬Q ⟶ ¬P$ $¬Q m$ is even, $m = 2k$ $¬P m^2 + 3$ is odd $= (2k)^2 + 3$ Help what I should do now after this step!
Amanda
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Prove that primes does not exists if we also add the products digits as an additional step for multiplication.

I would like to redefine multiplication by adding a new step. After taking the product, what if we sum the digits. Now the definition of primes would be modified in such that primes are natural numbers (excluding 0) that cannot be generated by our…
NoobCoder212
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Very trivial question about wave exponents being equal.

Let's suppose we know the following equality: $$\vec{v_1}e^{i(k_1x\omega_1t)}+\vec{v_2}e^{i(k_2x-\omega_2t)}=\vec{v_3}e^{i(k_3x-\omega_3t)}$$ is true for every real value of $x$ and for every positive real value of $t$. I think it is very trivial to…
davise
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What does "U.t.c." stand for in the context of a math proof?

What does "U.t.c." stand for in the context of a math proof? This abbreviation appears at the start of some (but not all) proofs in Desoer and Vidyasagar. "U.t.c." isn't searchable online (conflicts with temps universel coordonné), and isn't on…
MRule
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$-A$ is bounded from above if $A$ is bounded from below

There is a question in my textbook that goes as follows: Let $A \subset \mathbb{R}$ be a non empty-set that is bounded from below. Show that $-A$ = {$-x | x \in A $} is a non-empty set and bounded from above. This is my short proof. (In my…
user34
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Reusing symbols in proof by cases

In Book of Proof by Richard Hammack, part of a proof that divides into cases is written as such: Case 1. Suppose $m$ is even and $n$ is odd. Thus $m=2a$ and $n=2b+1$ for some integers $a$ and $b$. Therefore $m+n=2a+2b+1=2(a+b)+1$, which is odd (by…
Cynicrom
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Let $f(x)=7x+3$ and $g(x)=x^2$, prove that $f\in O(g)$ but $g\notin O(f)$

Let $F=\{f \; \vert f:\mathbb{Z}^+\rightarrow\mathbb{R}\}$, $O(g)=\{f\in F|\exists a\in\mathbb{Z}^+\exists c\in\mathbb{R}^+\forall x>a(|f(x)|\le c|g(x)|)\}$ $f(x)=7x+3$ and $g(x)=x^2$. Prove $f\in O(g)$ but $g\not \in O(f)$. I dont know what kind…
lightyourassonfire
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