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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Prove that if |, then |, for any , , , ∈ ℕ

Prove that if |, then |, for any , , , ∈ ℕ So I have, if abc|cd, then abc(k) = cd. I'm very confused on how to continue
user832463
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Proof: For all sets $A$, $B$, and $C$, if $A \setminus (B$ intersect $C) = \emptyset$, then $A \setminus B = \emptyset$ and $A - C = \emptyset$.

Here's what I have: The statement is true. Assume A, B, and C are sets, and that $A \setminus (B$ intersect $C) = \emptyset$. We will prove $(A \setminus B = \emptyset$ and $A - C = \emptyset)$ by assuming $(A \setminus B \not= \emptyset$ or $A…
user831363
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Proof: For all sets A, B, C, if A - (B intersect C) = empty_set, then A - B = empty_set or A - C = empty_set.

I'm having trouble wrapping my head around this question. Here is what I have for my proof so far: The statement is true. Assume $A, B, C$ are sets and $A - (B\cap C) =\varnothing$. Now we prove $A - B =\varnothing$ and $A - C = \varnothing$. I've…
user838441
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Let $A=\{3,4\}$ be a subset of $S=\{1,2,..., 6\}$. Let $n\in S$. Prove if $\frac{n^2(n+1)^2}{4}$ is even, then $n\in A$.

Let $A=\{3,4\}$ be a subset of $S=\{1,2,..., 6\}$. Let $n\in S$. Prove if $\frac{n^2(n+1)^2}{4}$ is even, then $n\in A$. I know this needs to be a proof by cases, and it should be "Assume $n$ is even. By definition $n=2k$ for $k \in \mathbb{Z}$.…
Wng427
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Choosing which method of proof to use

I have the following statement to prove Prove that if n is any integer then 4 either divides n^2 or n^2 − 1 I am new to proofs, how, when faced with a question like this, do I begin to decide which method of proof I should use?
Scott Adamson
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Prove that $\sqrt{x}+\sqrt{y}\neq \sqrt{x+y}$ where $x$ and $y$ are positive real numbers

I should do it by contradiction. Would finding a counterexample work? For example: Suppose $\sqrt{x}+\sqrt{y}=\sqrt{x+y}$. Then $\sqrt{4}+\sqrt{9}=\sqrt{4+9}$, which means $2+3=\sqrt{13}$ which is a contradiction. Is this a correct (even though no…
pipey
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I need help understanding how to write a proof. Time sensitive.

Let A, B and C be sets. Show that it is always true that A \ (B \ C) ⊆ (A \ B) ∪ C. Give an example of specific sets A, B and C to show that it is not necessarily true that A \ (B \ C) = (A \ B) ∪ C. I don't know where to start and I have never…
Clay
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Erroneous Proof

Would it be an erroneous proof if I only prove one case is true and then claim everything else to be true. For example, prove that $2x-4 > 0$ for all $x|x\in \mathbb{Z},$ $x>2.$ Would this proof be erroneous? The smallest value is $3.$ When $x=3,…
Joe
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Can it be proved that all mathematical statements can be proved true or false?

Given a mathematical statement, can it be always be proven to be correct or incorrect, or is it possible that a proof can not be created? Could all cases that could not be proven, be proven that no proof exists also? For example, with the Beal…
Eric Johnson
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C ∆ (A ∩ B) ⊆ A ∪ B what is the logical statement

Set C is symmetric difference of set A’s intersection of set B. therefore, is a subset of set A. the result is unioned with set B.
Nichole Reed
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(Correct Proof Writing) Proving basic limit theorem

I'm new to this site I'm starting to learn how to write proofs correctly and I will be very grateful if you help me find and correct the places where I write the syntax in the wrong way. Here's a basic theorem of limits, how correct is the writing,…
user814823
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Prove: If $x > 1$ and $y > 1$, then $xy >1$.

I am trying to prove that if $x > 1$ and $y > 1$, then $xy >1$. I am thinking that we can use proof by contradiction. So we can assume that $xy≤1$ and, $x>1$ and $y>1$. I got stuck and don't know what should be the next statement. Any comment and…
AYA
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Operator contained in a space of polynomials?

Consider $L^{2}([-1,1], \mathbb{C}),$ endowed with the inner product $\langle f \mid g\rangle=\int_{-1}^{1} f(x) \overline{g(x)} d x$ and with the associated norm. $\mathcal{P}$ is the space of polynomial of degree inferior to $2,$ taken as a…
phi
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For $a,b \in \mathbb{R}$, prove that $ ab \le a^2 + b^2$

For $a,b \in \mathbb{R}$, prove that $ ab \le a^2 + b^2$ Just what the title says. Im a bit stuck here. Edit:I'm thinking that since a and b are both reals, they can be either positive or negative, making ab either positive or negative. I also know…
kfox25
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Advice on proving statements without if-then form?

I do not know if this is the right place to ask but Googling failed. Whenever I do a "prove something" question, I try to formally restate in an if-then form. But when a statement can't be naturally restated to an if-then form, by process of…
Leon
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