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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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Decide if the statement " $n^2-1$ is multiple of $4$ if and only if $n-1$ is multiple of $4$" is true or false.

The statement is biconditional ( P $\Longleftrightarrow$ Q ) $n-1$ is multiple of 4 $\Longleftrightarrow n^2-1$ is multiple of 4 The statement is true if $\,$ P $\Rightarrow$ Q and Q$\Rightarrow$ P are true P $\Rightarrow$ Q $ n-1=4k, \, k \in…
B. David
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Constructing a bijective function + its inverse

I came across this question and wasn't too sure how to do it. Can anyone explain this? Construct a bijective function f : N → Z. Also, find its inverse. Any help is appreciated.
Enes Dal
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$f:\Bbb R \to \Bbb R$ s.t. $f(x) = 2x + \sin x -1$ then Find $f^{-1'}(-1)$

Let $f:\Bbb R \to \Bbb R$ s.t. $f(x) = 2x + \sin x -1$ then Find $f^{-1'}(-1)$ solution First, given function $f$ is differentiable at given domain of $x$ since $2x$, $\sin x$ and $-1$ is are all differentiable and also linear combination of these…
Beverlie
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multiply $2^{(a-1)b}$ by $2^b$ and get $2^{ab}$? How is this so?

I’m reading How To Prove It and in the following proof the author is doing some basic algebra with exponents that I just don’t understand. In Step 1.) listed below he is multiplying $2^b$ across each term in (1 + $2^b$ + $2^{2b}$ +···+$2^{(a-1)b}$)…
maybedave
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Prove that if $a \space | \space b$, then $a \space | \space 3b^3 - b^2 + 5b$.

I'm asked to prove that if $a \space | \space b$, then $a \space | \space 3b^3 - b^2 + 5b$. That is, if $a$ divides $b$, it also divides $3b^3 - b^2 + 5b$. My text does not have a solution to this problem, as it's even-numbered, so I was looking to…
Aleksandr Hovhannisyan
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My solving is correct? (Fourier - Bessel function)

My professor gives us the problem: Prove that $$ J_0(2\pi f_D\tau) \quad \underset{\mathcal{F}^{-1}}{\stackrel{\mathcal{F}}{\rightleftharpoons}} \quad \frac{1}{4\pi f_D\sqrt{1-(f/f_D)^2}}, $$ where $$ J_0(t) = \frac{1}{\pi} \int_0^\pi…
Danny_Kim
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Is my approach to this functions proof correct?

Prove or disprove. Given any set X and given any functions f : X → X, g : X → X, h : X → X, if h is one-to-one and h o f = h o g, then f = g. Let x belong to X We know that (h o f)(x) = (h o g)(x) (h o f)(x) = (h o g)(x) —> h(f(x)) = h(g(x)) Since h…
Hello
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Show that $\alpha\leq \beta$

Let $E$ be a non-empty subset of an ordered space. Suppose that a is a lower bound of $E$ and $\beta$ is a upper bound of $E$. Show that $ \alpha \leq \beta $. Proof: (1) If $\alpha$ is a lower bound of $E$ then $\forall x\in E\quad x\geq…
Roland
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Prove $B(P,r)\subseteq B(P,r')\implies r\leq r'$

Prove $B(P,r)\subseteq B(P,r')\implies r\leq r'$ where $B(P,r)$ is the set of points inside a circle with radius $r$ centered at $P$ and $d(P,Q)$ is the distance between $P$ and $Q$. So $$B(P,r)=\{x\mid d(P,x)\leq r\}$$ Proof: Assume…
Garmekain
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$\sup_{i \in \mathbb{N}} \sup_{j \in \mathbb{N}} B_{ij} = \sup_{j \in \mathbb{N}} \sup_{i \in \mathbb{N}} B_{ij}$

For any double sequence $B_{ij} \ i,j \in \mathbb{N}$ of real numbers we have $$\sup_{i \in \mathbb{N}} \sup_{j \in \mathbb{N}} B_{ij} = \sup_{j \in \mathbb{N}} \sup_{i \in \mathbb{N}} B_{ij}$$ Here is my attempt. $\forall m,n \in \mathbb{N}$ it…
Olba12
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Show that if $\lambda$ is an eigenvalue of real-valued matrix for $T\in V$, then $\bar{\lambda}$ is too

Let V be a finite dimensional complex valued space and $T\in \mathcal{L}(V)$ such that the matrix of $T$ (for some basis) has only real valued entries. If $\lambda$ is an eigenvalue so is $\bar{\lambda}$. Let $\lambda = a + b i$. Let $v \in V$ be…
Skurmedel
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Question about Euler proof of divergence of the sum of the reciprocals of the primes.

Consider the Euler proof : $$\ln\sum_{n = 1}^{\infty}\frac{1}{n} = -\ln\sum_{p}\frac{1}{1-p^{-1}} = \sum_{p}\left(\frac{1}{p} + \frac{1}{2p^2} + \frac{1}{3p^3} + \dots\right) = A + \frac{1}{2}B + \frac{1}{3}C + \dots = A + K,$$ where $K < 1$. My…
openspace
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How do you prove $B \setminus \cap_{i \in I} A_{i} = \cup_{i\in I} B \setminus A_{i}$?

I'm stuck on this proof. Especially in the $\implies$ direction. I've written the following but feel it is more just a restatement of the original equation than a proof. It goes from very specific (intersection) to general (union) and this is…
maybedave
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Prove that any integer $a$ can be uniquely expressed in the form $a=3^m+b_{m-1}3^{m-1}+...b_0$.

Problem: Prove that any positive integer $a$ can be uniquely expressed in the form $a=3^m+b_{m-1}3^{m-1}+...b_0$, where each $b_j=0,1,\text{ or }-1$. My Attempt: First we will prove that any positive integer $a$ has a unique representation in base…
Student
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Is this proof claiming that P(A union B) does not equal P(A) union P(B) correct?

Let $A$ and $B$ be finite sets and $\mathbb{P}(A)$ the power set of $A$. Then $\mathbb{P}(A \cup B) \neq \mathbb{P}(A) \cup \mathbb{P}(B)$ for some $A$ and $B$. Let $A$ be the set $\{1,2,3\}$ and $B$ the set $\{4,5,6\}$. Then $|A \cup B| = |A|+|B| =…
Adam
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