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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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Prove $ \bigcap_{n=1}^{\infty} I_{n}=\bigcap_{n=1}^{\infty}\left[-1,1-\frac{1}{n}\right]=[-1,0] $

From left to right $x \in \bigcap_{n=1}^{\infty}\left[-1,1-\frac{1}{n}\right] \quad \Longrightarrow \quad x \in[-1,0]$ Proof by contraposition. I have to prove the following implication $x \notin[-1,0] \Longrightarrow x \notin…
Sorry
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× ⊆ × . Prove ⊆ .

How would you go about proving this: × ⊆ × . Prove ⊆ . I said, because S * T is a subset of T * W then every element of S * T must exist in T * W but, that can only happen if S = T and T = W. Knowing that, S = W and thus, S is a subset of W. Is…
kgui
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How to prove $p ∧ (q ∧ r) ≡ (p ∧ q) ∧ (p ∧ r)$

As the title says, how to prove $p ∧ (q ∧ r) ≡ (p ∧ q) ∧ (p ∧ r)$ without using conjunctional laws? I did attempt this question on my own, but found myself running into road blocks.
Mark
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Verify that Sum of irrationals is not necessary irrational

$$a,b \in R/Q$$ Assume $$a+b = \frac{p}{q} $$ $$r=\frac{k}{j}$$ Now $$ra+rb =\frac{pk}{qj}$$ Clearly $\frac{pk}{qj}$ is rational, and both $ra$ and $rb$ are not which completes the proof.
Misha.P
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How do I prove this is correct when taken to infinity?

$\frac{35*87}{67*59}$ = $\frac{30*18.\overline{45}}{(39*18.\overline{45}) - 1}$ edited version: Step by step, how would I prove that the left and right sides are exactly equal using fractional math only (no decimal math)? $\frac{35*87}{67*59}$ =…
David_M
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How to prove $a - b = - (b - a)$ using the following laws?

I want to prove: $a - b = - (b - a)$ I am only allowed to use the following theorems: “Associativity of +”: (a + b) + c = a + (b + c) “Associativity of ·”: (a · b) · c = a · (b · c) “Symmetry of +”: a + b = b + a “Symmetry of ·”: a · b = b ·…
John
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Verifying proof that a shape is a parallelogram.

So I was tackling the following problem: And here is my working: However, I am unsure whether my proof is thorough as I think the shape could still be a rhombus? So I am just wondering whether the proof is satisfactory for part a.
Jamminermit
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Proving that "If $n^2$ is even, then $n$ is even" without using proof by contradiction.

If $n$ is an integer and $n^2$ is even, then $n$ is even I am reading a book on proofs and the above statement motivates the author to introduce Proof by Contradiction. I am a little confused as to why this proof motivates the introduction of a new…
S.C.
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Absurde Demonstration strategy

confused about the demonstration of the following statement : let a, b, c $\in R^{*+}$ . Demonstrate that: $a*b\geq1$ OR $a+b \leq \frac{1}{a}+\frac{1}{b}$ Demonstrate that ($a*b\geq1$ And $a+b \leq \frac{1}{a}+\frac{1}{b}$) if and only…
SAM.Am
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Nature of Proof by Contradiction

This is from a maths competition which is still probably taking place, so I don't think I will be able to release any specific details about it yet. Essentially, the question asked for a proof of $A\Rightarrow B$. This was however difficult so I…
T-bone
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Issue with Analysis Proof

The full problem I'm working on requires me to show 3 statements are equivalent; however, I am only having an issue with showing one particular implication. I want to make clear I am not looking for an answer, I simply want to know where my issue is…
Noaline
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A function equal to the limit a.e. is measurable

I think I did this right. Suppose that $F\in \mathcal{M}$ and that $\{f_n\}$ is a sequence of measurable functions that converge to a limit $a.e.$. Let $f=\lim f_n$ on $F$ and $0$ on $F^c$ where $F^c$ is null. Then $$\{x:\lim f_n=\pm…
CitizenSnips
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Let a and b be natural numbers. If gcd(a,b) > 1, then gcd(a^2, b^2) > 1.

Question Let a and b be natural numbers. If $\gcd(a,b) > 1$, then $\gcd(a^2, b^2) > 1$. My Attempt Contradiction: If $\gcd(a,b) > 1$, then $\gcd(a^2, b^2) = 1$ (since $\gcd$ cannot be less than $1$) for any natural numbers $a$ and b. Let $a = 2$…
Saransh Jain
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$(∪α Aα) × (∪β Bβ) = ∪(α,β) (Aα × Bβ)$

I am solving the following equation out of a book $⟦ A^{'}α{'}: α⊂A⟧$ and $⟦ B{'}β{'}: `β{'}⊂B⟧ $ (By the way, what does this notation mean? for any given alpha or beta follows that the given alpha or beta is part of the subset?) $(∪{'}α{'}…
Mad
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Proving that an odd positive integer raised to a positive power results in an odd number.

I want to prove the following statements: An odd positive integer raised to a positive power results in an odd number. And, An even positive integer raised to a positive power results in an even number. However, I am not sure how to do this…
Jamminermit
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