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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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$|A|<|B|$ and $|A|=|C|$ show $|C|<|B|$

I just want to make sure my reasoning is correct. I will express the part that I am confused about. Let $A,B,C$ be sets where $|A|<|B|$ and $|A|=|C|$, show $|C|<|B|$. My Work Because $|A|<|B|$ there is an injective but not surjective function $…
Tsangares
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Could someone verify proof regarding equivalence relation and classes

Exercise 11.3.4 from Book of Proof by Richard Hammack: Proof that R is an equivalence relation: First we show $xRx\space\space \forall x \in A$. From the definition of $R$, $xRx$ if $x \in X$ for some $X \in P$. Now, since $x \in A$, it has…
Max
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Elementary proofs help

I'm taking Principles of Mathematics this semester and I came across a problem, but I don't know whether my proof is valid or not. I was hoping you could help me out. It goes like this: Let $x$ be a natural number. Prove or disprove:…
Alex Della Torre
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Proof that set $F$ is infinite.

I am doing some homework, let me know if this makes sense: Question Let $F \subset \mathcal P(\mathbb N)$ be the set of all finite sets of $\mathbb N$. Construct an injection $\phi: F\rightarrow \mathbb N $. What does this say about the cardinality…
Tsangares
  • 797
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Homer Simpson's Fermat equation

Disprove the following equation $3987^{12} + 4365^{12} = 4472^{12}$ First, since both the two numbers on the LHS were odd and the RHS was even, I tried dividing by 3 and found $3 \mid 3987$ and $3 \mid 4365$ so $3 \mid 3987^{12}$ and $3…
blablabla
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Is this proof of the fact that only 1 and -1 divide 1 correct?

The only numbers that divide $1$ are $1$ and $-1$. If $x$ divides $1$, then \begin{equation} xk=1 \end{equation} for some $k$. To find all numbers that divide 1, we only need to find all integer solutions to the equation above. We argue by cases.…
Adam
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Suppose $A=\{(m,n)\in\mathbb{N}\times\mathbb{R}:n=\pi m\}$. Is it true that $\vert\mathbb{N}\vert=\vert A\vert$

Can someone take a look at the proof I've constructed below? Does this work and does anyone have any suggestions? Suppose $A=\{(m,n)\in\mathbb{N}\times\mathbb{R}:n=\pi m\}$. Is it true that $\vert\mathbb{N}\vert=\vert A\vert$? My answer: Yes, this…
ClownInTheMoon
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Is it 'not mathematical' to compare the L.H.S. and R.H.S in such type of equations?

$$x+\frac{1}{x}=25 + \frac{1}{25}$$ The solution is very simple. But the problem is whether my solution is correct or not. I did it by simply comparing the LHS and the RHS. Thus, I got $x=25$ or $\frac{1}{25}$. But my book does it in this…
Soham
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Proof that $5x^2 + 4y^3 = 51$ has no solutions for $x,y \in \Bbb Z^+$

So I have been given this question to answer: Give a proof by cases to show that the equation $5x^2 + 4y^3 = 51$ does not have any solution $x,y \in \mathbb Z^+$ I am assuming that I could give two cases for this problem: Express everything in…
Jake0991
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Prove that $3^1+3^2+3^3+3^4+\cdots+3^n=\frac{3^{n+1}-3}{2}$ (suggestions for improvement on basic induction style/proof)

Please see my proof to the following proposition below. From a standpoint of critiquing does this seem like a great execution or would someone feel that this proof was overly cumbersome? Specifically for the purposes of marks in a class how would…
ClownInTheMoon
  • 1,987
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Suppose $\alpha , \beta $ and $\gamma$ are functions if $\alpha\circ\gamma = \beta\circ\gamma$ and $\gamma$ is bijective, prove that $\alpha = \beta$

So what I did was say that for every $x$ in $\gamma$ we have $\alpha(\gamma(x))=\beta(\gamma(x))$ and since $\gamma$ is bijective $x$ gets mapped to only one element of the range and will call this $y$. Now we have $\alpha(y)=\beta(y)$ and then i…
L. Johnson
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Proof for integration by substitution

I have a question about the proof for integration by substitution. It starts the following way: Let $ \phi: [a, b] \rightarrow [c, d]$ be continuously differentiable and $f: [c, d] \rightarrow \Bbb R$ continuous. Furthermore, let $F: [c, d]…
Julian
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Prove If a,b, c in N, then lcm(ca, cb) = c lcm(a,b).

Prove: If $a,b,c$ in $\mathbb N$, then $lcm(ca, cb) = c \cdot lcm(a,b)$. Assume $a$,$b$,$c \in \mathbb N$. Let $m = lcm(ca,cb)$ and $n = c\cdot lcm$. Showing $n = m$. Since $lcm(a,b)$ is a multiple of both a and b, then by definition $lcm(a,b) = ax…
alan
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When is a fact 'obvious enough' that it does not need proving?

Here is an example to better explain the question: Theorem: If $n$ is any integer, then $3n^3 + n + 5$ is odd Counterexample: $n = 2k + 1$ $3n^3 + n + 5 = 3(2k + 1)^3 + (2k + 1) + 5$ = odd + even + $5$ = even Must I prove that for any value of…
sammy
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Proper presentation for proof of $y = x^3 - 3x + 1$ having only irrational roots.

Considering the assertion: The polynomial $x^3 - 3x + 1$ has no rational roots, the following is a proof by contradiction: Let a root of $x^3 - 3x + 1$ be written in the form of $\frac{p}{q}$ where $p$ and $q$ are coprime. Thus $\frac{p^3}{q^3}$ -…
Lagrangian
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