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Questions tagged [proof-verification]

For questions concerning a specific proof or a specific solution, asking for verification, identifying errors, suggestions for improvement, etc. (You should not use this tag if the question does not contain a proposed proof/solution.)

For questions concerning a specific proof (or a proof sketch) or a solution to some problem; asking a question with this tag indicates one would like answers to respond broadly as to the following:

  • Verification of the proof/solution;
  • Identifying errors in the proof/solution;
  • Suggestions for improving the proof/solution;
  • Alternative approaches.

Also, consider the related tags and .

22798 questions
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Proving operations $r_h$ and $r_v$ commute,

How would you prove the following proposition... The operations $r_h$ and $r_v$ commute, that is, $r_hr_v=r_vr_h$ where $r_h$ is a horizontal reflection and $r_v$ is a horizontal reflection. I can see it is true if you were to draw out say a…
user6259845
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Proof that $\sqrt{x}$ is Unbounded!

I need help making my proof strong/valid! I am new to proofs. The question was:Let $A=\{x\in \mathbb{N} | \sqrt{x}\in \mathbb{N}\}$. Prove that A is not bounded. Proof: We must show that for all $m\in \mathbb{N}$, we can find an $x_0 \in B$ such…
futuremathteach
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Proving the formula of function graph

i have to prove the following statement: $\mathbb \forall a \in A, \exists ! b \in B : (a,b) \in \Gamma $ where Gamma is the graph of a function. I proceeded in this direction (first time using absurd proof): Lets say that a function is not a unique…
Federico
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Deriving Variance for a General Poisson Random Variable

Suppose I wanted to prove, using infinite series, that the variance of a Poisson random variable $X$ with parameter $\mu$ is $\hbox{Var}[X] = \mu$. I'm having some trouble constructing this proof with a change of variables, and I think I must be…
user465188
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how to prove that a natural number n > 1 is prime if and only if n divides (n-2)! - 1?

how to prove that a natural number n > 1 is prime if and only if n divides (n-2)! - 1? I know it is a 'iff' questions so that it need to be proved by both directions, and I tried to prove by contradiction or contrapositive but still did not figure…
Zhenqing Xu
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Is $47$ the largest whole number?

I was shown the following proof by contradiction, which somehow shows that $47$ is the largest whole number. Obviously this is not true, but I am not exactly sure where the proof goes wrong. Here it is: Assume $47$ is not the largest whole number.…
Madhav Nakar
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Right solution?

I am trying to solve an equation in the research article. $f(g)$ is the pdf below: \begin{align} f(g) = \frac{(K+1)e^{-K}}{\bar g}exp\Bigg(-\frac{(K+1)g}{\bar g}\Bigg) I_o\Bigg(\sqrt\frac{4K(K+1)g}{\bar g}\Bigg) \end{align} $I_o(.)$ is the zeroth…
SJa
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Sum of Element in Subset of A is divisable by n.

I need some help with the following problem: Question: Let $n \in \mathbb{N}$ and $A$ $\in$ {$a_1,a_2,\ldots,a_n$} such that there are $n$ integers in $A$. Prove that there exists a subset $S$ of $A$ such that the sum of the elements in $S$ is…
Sanguine Salvo
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Function and Equivalence Classes question

I have the following question: Question: For the set $\theta=\{(X,|X|):X\subseteq\mathbb{Z}_5\}$, what is its domain and range? The Domain stated in the solution from the textbook is: $\mathcal{P}(\mathbb{Z}_5)$ as in the Power set of…
Sam Kay
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setting of this induction proof

I would like to see if this is a correct induction proof and whether or not this is a good setting out of it A sequence is defined by $$a_n = a_{n-1} + a_{n-2} + a_{n-3}$$ for $n\geq 3, a_0 = 1, a_1 = 2, a_2 = 4$. Prove that $a_n \leq 4^n$ for all…
OneGapLater
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Prove the following statement: If $n$ and $m$ are nonzero integers, then $n^2-m^2 ≠ 1$.

Here is my attempt. Proof: By way of contradiction, suppose m and n are nonzero integers and that $n^2-m^2 = 1$. Then, $(n-m)(n+m)=1$. That is where I get stuck, apparently we are supposed to show $(n-m)=(n+m)$ but I don't see how that would be…
MANONMARS45
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Proving a sequence is not a cumulative sequence

An infinite sequence of sets $S_2,S_3,S_4,\ldots$ is called a cumulative sequence if the following condition holds: $$\exists m\geq 2 \quad \forall n>m \quad S_n\subseteq S_2\cup S_3\cup S_4\cup \ldots \cup S_m. $$ Prove that the sequence…
Natash1
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Injective Function and Pigeonhole principle.

I'm reading the Book of Proof textbook and I got stuck on the following example question: Proposition: If A is any set of 10 integers between 1 and 100, then there exist two different subsets X ⊆ A and Y ⊆ A for which the sum of elements in X equals…
Sam Kay
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Relations: Reflexive and Symmetric Questions

I'm really confused about the concept of Reflexive and Symmetric relations. for an example from my textbook: Let A = {b, c, d, e} and the relation on 'A' be defined as R = {(b,b),(b,c),(c,b),(c,c),(d,d),(b,d),(d,b),(c,d),(d,c)} The book claims that…
Sam Kay
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Show that $a^2$ congruent 0 (mod 4) or $a^2$ congruent 1 (mod 4).

Proof: Suppose for the sake of contradiction, there is an integer a such that $a^2$ congruent $0 \pmod {4}$ and $a^2$ congruent $1 \pmod {4}$. Then $(a^2)-0=4k$ and $(a^2)-1=4l$ for some $k,l$ members of the integers.…
Gurvir Dhami
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