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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 this proof optimized well enough?

Suppose a,b,c,d € R. Then If a+c=b+c, then a=b ( this is the question) My answer; Assume a+c = b+c then a+c+(-c)=(-c)+b+c by (Existence of Additive Inverses) Thus a+(c+(-c)=((-c)+c)+b by (Associativity of Addition) Since (c+(-c))=0 by (Existence of…
Scott
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The interval [0,1] andd [3,5] are equivalent. Is my proof correct?

The intervals $[0,1]$ and $[3,5]$ are equivalent. My proof goes like this. Proof. To show that the two sets are equivalent, we should show a bijection between them. Consider the function $f:[0,1] \to [3,5]$ such that $f(x)=2x+3$. Since $f$ is …
Hindi ko po alam
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Proof going in Circles

I am trying to show that if $m \in \mathbb{Z}$ and $m \ne 0$, then there exists an integer $k > 1$ such that $m \mid k$. However, I seem to be going in circles and arriving at incorrect conclusions. If $m \ne 0$, then there exists some integer, $n$…
Math1
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Expression Output - Unsure how to verify solution

Okay - so, I have the expression $5x^2+2x-3$ and have found that odd integers ($2x+1$) output an even number ($2\times integer$). But, how do I know this is the LARGEST set of integers that outputs an even number?
Math1
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Sum of any two consecutive squared integers mod 4 = 1

So today we were trying to prove algebraically that two consecutive integers n, n+1 where each is squared mod 4 is 1. We got quite far, but I can't for the life of me find the notes which we made. Not much more I can write really, if I find my notes…
Jacob Garby
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Prove that if $(a,b)=1$ and $c|a+b$ , then $(a,c)=(b,c)=1$.

Problem: Prove that if $(a,b)=1$ and $c|a+b$ , then $(a,c)=(b,c)=1$. My Attempt: Let $(a,c)=e$ and $(b,c)=f$. Then $e|a$ and $e|c$. This implies that $e|a+b$, which further implies that $e|b$. Thus we deduce that $e\leq f$ (from the fact that $e|b$…
Student
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Linear Transformation holding under scalar multiplication

In the following proof I am trying to show that Prove that the function $T : R^3 → R^3$ defined by $T(w) = Proj_π(w)$ is a linear transformation. My textbook has shown that it holds under addition; now I want to show it holds under scalar…
bjp409
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Proof that $\exists A > 0$ such that $a_n+A > 0, ∀ n ∈ \mathbb{N}+$ for a bounded sequence $(a_n)_{n∈\mathbb{N}+}$

I'm trying to prove that $\exists A > 0$ such that $a_n+A > 0, ∀ n ∈ \mathbb{N}+$ for a bounded sequence $(a_n)_{n∈\mathbb{N}+}$. My proof so far is as follows: If $(a_n)_{n∈\mathbb{N}+}$ is bounded $\Rightarrow$ $\exists U∈\mathbb{R}$ such that…
aL_eX
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Review my proof on $A \subseteq B$ iff $A \cap B = A$

I have a terrible time converting my thought process into a proof. I can see how this statement is true, but writing out an actual proof I get lost pretty easily. This is what I have: Assume that $A \subseteq B$ then $A \cap B = A$. We will show…
Michael Rector
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Induction technique on the fibonacci sequence

\begin{equation} F_n=\frac{(\frac{1+\sqrt{5}}{2})^{n}-(\frac{1-\sqrt{5}}{2})^{n}}{\sqrt{5}} \end{equation} Proof: Let n=1…
HighSchool15
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Showing the sets are equivalent using set builder notation.

Proof: Just observe the following sequence of equalities. \begin{align*} A \times (B - C)&=\{(x,y):(x\in A)\land(y\in(B-C))\} \textbf{(def. of $\times$)} \\ &=\{(x,y):(x\in A)\land (y\in B)\land(y\notin C)\} \textbf{(def. of -)} \\ …
HighSchool15
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If $p$ and $q$ are prime numbers for which $p < q$, then $2p+q^{2}$ is odd.

If $p$ and $q$ are prime numbers for which $p < q$, then $2p+q^{2}$ is odd. Suppose $p$ and $q$ are prime and $p
HighSchool15
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$\lambda \in K$ is an eigenvalue of $\phi$ iff $\lambda$ is a root of the characteristic polynomial $P$

Statement: Assume $V$ is a vector space over a field $K$. Let $\phi: V \rightarrow V$ be a linear map. Then $\lambda \in K$ is an eigenvalue of $\phi$ iff $\lambda$ is a root of the characteristic polynomial $P$. Proof: Let $M$ be the matrix of…
Julian
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For all positive real numbers $x$, if $x$ is irrational, at least one of the numbers $x+\sqrt{2} $ and $x^2 - 2$ is irrational.

How to prove this theorem? If I use contrapositive, the theorem becomes "If at least one of the numbers $x+\sqrt{2}$ and $x^2 - 2$ is rational, $x$ is rational". I have no idea how to prove the two numbers are rational.
Matthew
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Why this proof is correct?

Irrationality of $e$ I saw this proof and it looks exciting, but I don't know why this part is correct: $$(2k - 1)!e^{-1} \in \mathbb{Z}$$
openspace
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