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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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Why is $i^2$ not equal to $1$?

I've only recently started learning about imaginary numbers, and there is one thing I cannot really wrap my head around: $i^2 = i*i = {\sqrt{-1}} * {\sqrt{-1}} = {\sqrt{(-1) * (-1)}} = {\sqrt{1}} = 1$ I'm aware that by definition $i^2 = -1$, but as…
fygesser
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Suppose $A \precsim B$ and $C \precsim D$. If $A = \varnothing$, can $\text{}^A C \precsim \text{}^B D$ be true?

For any sets $A$ and $B$, the set of all functions from $A$ to $B$ is denoted $\text{}^A B$. If there is a one-to-one function $f : A \rightarrow B$, $A \precsim B$. Suppose $A \precsim B$ and $C \precsim D$. If $A = \varnothing$, can $\text{}^A C…
user231595
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Did I prove correctly that if $A∼B$, then $\wp(A)∼\wp(B)$?

Suppose $A \sim B$. Then, there is a one-to-one and onto function $f : A \rightarrow B$. Since $f$ is one-to-one and onto, $f^{- 1} : B \rightarrow A$ exists. Let $g : \wp(A) \rightarrow \wp(B)$ be defined as $g (A) = \{ f (a) |a \in A \}$ and $h :…
user231595
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Is my understanding of this proof correct?

Given the definition: A real number $x$ is said to be positive if $0\lt x$ and negative if $x\lt 0$, and the Axioms of order (Trichotomy, Transitivity, Monotonicity of addition and multiplication), prove that $0\lt 1$. The approach that I have come…
user185744
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Fermat's theorem on two squares - what do I missing?

In Wikipedia there's a list of quite non-trivial and beautiful proofs of Fermat's two squares theorem. Actually I'm a bit surprised because this fact belongs to a very small set of mathematical fact that I, well, "see" and understand. Here's how I'm…
shabunc
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Normal Matrix with Real Eigenvalues is Hermitian

Let $A$ be a normal matrix. Then I want to show that, if $A$ has real eigenvalues, $A$ is Hermitian. (Notation: * denotes the complex conjugate, T denotes the transpose, and $\dagger$ denotes the conjugate transpose.) Suppose that $A$ has only real…
wordywolf
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Is non-paralellism transitive?

I've been trying to check if non-paralellism is transitive. At the moment, I know it's symmetric. But I have no idea on how to prove that it's transitive. I did the following: $$(a \not\parallel b) \wedge (b\not\parallel c)$$ And then, if…
Red Banana
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Which of the following sets are countable?

a) $[0,1] \cap \mathbb Q$ b) $P(\mathbb Q)$ c) $\mathbb R \setminus \mathbb Q $ d) $\{(a, b) ∈ \mathbb R\times\mathbb R | a, b \in\mathbb N\}$ I answered a) and d) a) any intersection between two sets where one if finite must be countable b) by…
Eddard
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Let $n$ and $p$ be positive integers. Show that $n$ can always be expressed in the form $n=pq+r$

I would have thought this would have been on here somewhere. Here I go. Let $S$ be the set of positive integers $n$ which can be expressed in the form $n = pq + r$ where $ 0 \leq r < p.$ where $p$ is a positive integer and $q,r$ are natural…
user197848
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Spot the error in experimenting with contradiction on 5's rationality.

Let $5=\frac ab$ $\forall\ a,b\ \epsilon\ N$. And $(a,b)=1$ Squaring both sides, $25b^2=a^2$ Thus, $25|a^2$; $25|a$ So $a=25m$ Substituting, $25b^2=25^2m^2$ So $b^2=25m^2$ So $25|b$ (By the same logic used before). But are assumption is…
Aditya Agarwal
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Proof Check In: Prove that $(\mathbb{Z}_n, +)$, the integers (mod $n$) under addition, is a group.

I received some help and direction on this from some users a few days ago, and have tried to take that information and craft it into something proofy. I would appreciate general suggestions, edits, and verification for for my proof-sketch. Please…
Mr. Meeseeks
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Replacing occurrences of the same integer as follows: is it legitimate in subsequent steps of a proof?

I need to spot the incorrect step in a spoof (false proof) and the first two lines are: $-5 = -5$ $-7+2 = -4-1$ Of course both the right- and left-hand side of the equation in the second line are equal to $-5$, as in the first equation. But is it…
user252639
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Upper Bounds Of Integers Intersection

Prove\Disprove: $A$ is bounded from above $\iff$ $A\cap \mathbb{Z}$ is bounded from above. Let $A=\{a\in \mathbb{Q} \setminus \mathbb{Z}: a<0\}$ is bounded from above, $A\cap \mathbb{Z}=\emptyset $ and $\emptyset$ is not bounded from above Is it…
gbox
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Let S be the set of stars in our galaxy. There is same number subsets as functions f : S --> {a,b}?

Question: Let $S$ be the set of stars in our galaxy. There is exactly the same number of subsets of stars in our galaxy as there are functions $f:S \to \{a,b\}$ . My solution is; True.However, I'm confused with how to prove it. I know it can be…
Legion
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Prove that a function $f:X \to Y $ is injective if and only if $\forall x_1, x_2 \in X$ where $f(x_1) = f(x_2)$ implies that $x_1 = x_2$

Prove that a function $f:X \to Y $ is injective if and only if $\forall x_1, x_2 \in X$ where $f(x_1) = f(x_2)$ implies that $x_1 = x_2$ Taking the contrapositive we get (this is the step I'm a little hazy on) For $x_1, x_2 \in X$ where $x_1 \neq…
RhythmInk
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