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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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Is Finite Cartesian Product of Connected Spaces is Connected?

A finite cartesian product of connected spaces is connected. This proposition is given as True in the topology textbook. I'd like to prove it via contradiction. First, let's suppose those space(finite cartesian product of connected spaces) is…
snapper
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How to prove a piecewise function is 1-1

$$f(x) = \begin{cases}x-1,&\text{ if }x\text{ is even}\\ x+3,&\text{ if }x\text{ is odd}\end{cases}$$ I know that I need $4$ cases in order to prove this function is one -to-one I have proven them all. Two of the cases showed the function is …
jeff c
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Getting a contradiction based on assumption?

If the functions $f$ and $g$ are functions that their output is the cardinality of some set associated to its input (the exact definition of these functions is irrelevant here), does $\forall x\in X:f(x)\leq g(x)$ and $\sum_{x\in X}f(x)=\sum_{x\in…
Garmekain
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Help - Prove using cases

for every natural number n ≥ 1 the number $n^2 + n + 4$ is not a prime number Hi there, I am trying to prove this using a proof by cases. I am just simply confused on how to do this or start this off. Any help is appreciated.
Layken
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Invertibility of Restricted Incidence Matrix of Connected Graph

Let $G$ be a connected graph with n vertices. Suppose a subset $S$ ⊂ $E(G)$ with $|S| = n − 1$ defines a spanning tree in G. Let $Q_S$ be the restriction of the incidence matrix $Q$ of $G$ to the columns indexed by $S$. Show that $Qˆ{ _S} = Q_S−…
Beverlie
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Check My Proof: if $a$ is even then $9(a +5)$ is odd

Just want to make sure I am doing this right. If $a$ is an even integer then $9(a + 5)$ is odd If $a$ is even, $a = 2k$, therefore, $9(a + 5) = 9(2k + 5)$ which is odd.
randochick
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How to analytically prove this result?

Let x and y coordinates be $$x = a_1 cos(\theta_1)+a_2cos(\theta_1)cos(\theta_2) - a_2sin(\theta_1)sin(\theta_2)$$ $$y = a_1 sin(\theta_1)+a_2cos(\theta_1)sin(\theta_2) + a_2cos(\theta_2)sin(\theta_1)$$ How can I analytically prove that if $a_1>a_2$…
csg
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Finding $\theta$ given $(x,y)$ no calculator used

Suppose theta is the angle in standard position whose terminal sides coincide with the point $P(3,4)$. Find $\cos\left(\dfrac{\theta}{2}\right)$. Solution: I tried using the $\arctan$ formula to find the angle that the coordinates will yield, but we…
shhh
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Not sure where I'm wrong, regarding the infinitesimal and .999...=1

Firstly I'm aware of the proofs/reasons regarding .999...=1. I'm not asking for anyone to reference or reiterate them but rather to look at my proof in isolation and help me understand my own mistakes and fallacies. Another disclaimer I suppose;…
Georg Anatoly
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Proof of if $3(x-y)$ is even, then $x$ and $y$ have the same parity

I am asked: Determine if the following statement is true or false by considering its contrapositive. Prove the statement if it is true. If $x$ and $y$ are two integers for which $3(x-y)$ is even, then $x$ and $y$ have the same parity. Here's my…
Brandon O'Neil
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VERIFICAATION: Find the 9th term from the end of the AP 5, 9, 13,...., 185.

Given: AP $\implies$5, 9, 13, ..., 185 Required: 9th term of AP from last Solution: Let a be the first term, d the common difference, l the last term We have d= a2-a1=9-5=4 d=4 Since an=a+(n-1)d $\implies$ $ l= 5+(n-1)*4=185 $ $\implies$…
PlopMon
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Suppose E ⊆ Z is nonempty and bounded above. Show that sup(E) ∈ E. In particular, sup(E) ∈ Z.

I think that since E is a subset of Z than all the element must be integer.then sup(E) must exist in E. I really do not know how to prove this. could someone help?
Zibo Hong
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Is this function injective? + Proof

I think this function is not injective, but I am unsure if I've correctly proven that. Determine if the following statement is true or false and provide a proof to justify the answer. \begin{align*} g: \mathbb{R} & \to \mathbb{R} \\ g(x) &=…
Brandon O'Neil
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Is $g:\mathbb{P}_1 \rightarrow \mathbb{P}_2 ,g(p)(x)=\int_0^x p(t)dt$ injective?

I think this function is injective, but had a tough time proving it. Here's my attempt. Proof: Let $(x_1,x_2)$ be arbitrary elements of $\mathbb{P}_1$. Assume $g(x_1)=g(x_2)$, i.e. $\int_0^x x_1dt=\int_0^x x_2dt$. Integrating yields…
Brandon O'Neil
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