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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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(Proof Verification) $E(X) = \int_0^{\infty}(1-F(x))dx$

Let continuous random variable $X \ge 0$ and $E(X) \lt \infty$. Let cumulative density function $F(X)$ is differentiable at all points of X, show that $E(X) = \int_0^{\infty}(1-F(x))dx$ Since $F'(x) = f(x)$, $E(X) = \int_0^{\infty}xf(x)dx =…
Beverlie
  • 2,645
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Proof by induction of inequality

Let p(n) be the mathematical statement: $2^n \leq 2^{n+1} - 2^{n-1} - 1$. Base Case: When n = 1 we have $2^1 \leq 2^{1+1} - 2^{1-1} - 1$ which simplifies to $2 \leq 4$. So P(1) is correct. Induction hypothesis: Assume that P(k) is correct for some…
Seth Killian
  • 251
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Solution Verification $(1+t^2)y' +4ty =t, y(1) = 1/4 $

$(1+t^2)y' +4ty =t, y(1) = 1/4 $ Given equation can be transformed into $(1+t^2)y' = (1 - 4y)t$ then $\frac{dy}{dt} = \frac{t}{1+t^2}(1-4y)$ then $\frac{1}{1-4y}dy = \frac{t}{1+t^2}dt$ then by integration at both sides respectively, one can get $\ln…
Beverlie
  • 2,645
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If A\B ⊆ C ∩ D and x ∈ A. Prove that if x is not in D then x ∈ B

A\B ⊆ C ∩ D and x ∈ A . I must show that if x $\notin$ D then x $\in$ B. So far, I am thinking that, $$\text{x} \in \text{A }\land \text{x} \notin \text{B} \implies \text{x}\in C \land \text{x}\in D $$ So if $$\text{x} \notin \text{D} \implies…
Math2Hard
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How does $2^{3b}$ - $2^{(a-1)b}$ = 0?

I have a proof and am unsure of the algebra to get from Step 2.) to Step 3.) below. When I subtract ($2^b$ + $2^{2b}$ + $2^{3b}$ + $2^{ab}$) - (1 + $2^b$ + $2^{2b}$ + $2^{(a-1)b}$) I do the following: Remove the ellipse and assume 4 elements in…
maybedave
  • 509
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Lemma on arithmetic and geometric means

Randomly thought about this in bio class today, did some quick work. Is this identity known and does it have any applications? Let $\text{am}(a,b)$ denote the arithmetic mean of two numbers. Let $\text{gm}(a,b)$ denote the geometric mean of two…
Leonidas Lanier
  • 4,149
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Proving that the additive groups $\mathbb{Z}$ and$\mathbb{Q}$ are not isomorphic.

I'm asking this question to review the second answer, the one with 7 votes, posted in response to this question. Since the thread is very old, I'm not sure if I'll get a response to the comment I posted. Isn't the proof given in the answer…
Junaid Aftab
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(Verification) Ordered Basis Consists of Subspace $\rightarrow$ $Direct\;Sum$ of Subspaces

Let $W_1, W_2, W_3,..., W_k$ be subspaces of a finite-dimensional vector space V. Claim There $\exists $ $\gamma_1 \cup \gamma_2\cup..\cup\gamma_k$ which is an ordered basis for $V$ ($\gamma_i$ is an ordered basis for $W_i$) $\rightarrow$ $\;\;$$V…
Beverlie
  • 2,645
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Is this proof actually true?

Link If a tribonacci sequence has 20 as its second seed and 17 as its third seed, find all positive integers that can be its first seed so that 2017 appears as a term somewhere in the sequence. Note: Tribonicca is the sequence of number the…
bio
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Disprove "if and only if statement"

I know that this statement is false, but I am having some trouble disproving it. If $x$ and $y$ are integers, then $x|y$ if and only if $x^2|y^2$.
Bob Rancando
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Is my approach to this set theory proof correct?

Prove: For all sets A, B, C, if B ∩ C ⊆ A, then (C - A) ∩ (B - A) = ∅. Since B ∩ C is a subset of A, B is a subset of A. Since B ∩ C is a subset of A, C is a subset of A. Since B is a subset of A, subtracting A from B will result in the empty…
Hello
  • 509
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Proof of Euclid's Lemma through contradiction

I tried to prove Euclid's Lemma. Please tell me if it's correct, I'm new to proofs. Euclid's Lemma: Let $p$ be a prime number and $a$ and $b$ be natural numbers greater than 1, then if $p|ab$ we know $p|a$ or $p|b$ I rewrote this as: $[p$ prime…
Strîmtu Gheorghe
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Proof of $f(z)=(z-\lambda_{2})\cdot\cdot\cdot(z-\lambda_{m})$ is equal to zero when applied to operator $T$ with $n$ distinct eigenvalues.

$\mathbb{F}=\mathbb{C}$, Dim$V=n$ and $T\in\mathcal{L}(V)$ has $n$ distinct eigenvalues $\lambda_{1},..., \lambda_{n}$. Let $f$ be the polynomial defined by $f(z)=(z-\lambda_{2})\cdot\cdot\cdot(z-\lambda_{m})$. Prove that $f(T)=0$ My proof: First,…
rocksNwaves
  • 971
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3 answers

Am I solving this inverse function problem correctly?

I need to find the inverse of this funtion $f(x)=\frac{e^{2x}+1}{e^{2x}-1}$. This is how I did…
Andres Romero
  • 415
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There exists an integer k such that $n = 3k+1$. Then $n^2 = (3k+1)^2 =9k^2 + 6k + 1 = 3 (3k2 +2k)+1$.

Consider the following proof fragment. There exists an integer $k$ such that $n = 3k+1$. Then $n^2 = (3k+1)^2 =9k^2 + 6k + 1 = 3 (3k^2 +2k)+1$. For each of the statements, $(a), (b), (c)$, below, answer the following. Does the fragment provide a…
Hidaw
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