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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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I have a problem understanding conceptually > using natural numbers

I am learning proofs with $\mathbb N $. I don't have significant problems using the axioms to prove propositions, I have a problem understanding certain axioms and the definition of >. 1) If $m,n \in\mathbb N$, then $m + n \in\mathbb N$ 2) If $m,n…
Johnathan
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Using the fact that 2 is prime, show that there do not exist integers p and q such that $p^2=2q^2$

Using the fact that 2 is prime, show that there do not exist integers p and q such that $p^2=2q^2$. Demonstrate that therefore $\sqrt2$ cannot be a rational number. Second attempt: Suppose $p^2=2q^2$,…
Math Major
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Which of the following subsets of $\mathbb R^2$ with the indicated operation, is a group? Which is an abelian group?

$(a, b) * (c, d) = (ac, bc + d),$ on the set $\{(x, y) \in \mathbb R \times \mathbb R: x \neq 0\}$. $(a, b) * (c, d) = (ac, bc + d) = (ca, da + b) = (c, d) * (a, b).$ Elements here commute about $*$. $((a, b) * (c, d)) * (e, f) = ((ac, bc + d)) *…
AbstraktAlgebra
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Proving $<$ is transitive on $\mathbb{Q}$.

I feel a little bit stupid asking this; I am asked to prove that, for all rational numbers if, x < y and y < z then x < z. I have said this; $ x + 0 < y $ $ x - z + z < y$ $ x - z < y- z $ but $ y - z < 0$ so $ x - z < y- z $ implies $ x - z < 0…
user197848
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Is the following subset of $\mathbb R \times \mathbb R$ with the indicated operation a group? Is it an abelian group?

$(a, b) * (c, d) = (ad + bc, bd),$ on the set $\{(x, y) \in \mathbb R \times \mathbb R: y \neq 0\}$. $(a, b) * (c, d) = (ad + bc, bd) = (cb + da, db) = (c, d) * (a, b).$ Commutativity holds. $((a, b) * (c, d)) * (e, f)) = ((a, b), f) + ((c, d),…
AbstraktAlgebra
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A proof involving identity permutation and even number of transpositions

I am trying to understand this lemma. I'll use variables $a$ and $b$ in the same way they are used in the linked proof. First we write down the identity permutation as a composition of transpositions. Then, take one of the transpositions which…
Passport
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How do I solve these bijections?

Let $f$ be a bijection from a set $A$ to a set $B$. The inverse of $f$, noted $f^{-1}$ is the function that assigns to an element $b \in B$ the unique element $a \in A$ such that $f(a)=b$. Hence $f^{-1}(b) = a$ when $f(a) = b$. Let $f$ be a…
dov rosenfeld
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a proof for a probably common problem?

Can someone provide a proof for the following problem? I know that this might be a common proof to some common problem that I am yet to know, and that if someone would leave a proof it would give me a deeper understanding of powers. $$x^{-n}=\frac…
MA-The-Matical
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Prove by contradiction $a \in C$, if $a \in A \land a \not\in B \setminus C$

This is the exercise I have: Suppose that A ⊆ B, a ∈ A and a $\not\in$ B\C. Prove by the method of contradiction that a ∈ C Proving by contradiction means that if I find a contradiction trying to prove the opposite of what I want to prove, I prove…
user168764
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Proving a increasing function with algebra

I'm attempting to prove a quadratic function is increasing without any calculus, just using algebra facts. My question: Consider the function $g(x) = (x + \dfrac{1}{2})^2 + \dfrac{7}{4}$ Prove that For every $x_1$ and $x_2$ in the interval [2,4], IF…
Johnny Andrea
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Please help me finish this proof - the midpoints of the 4 sides of any quadrilateral are the vertices of a parallelogram

a) Let $A$ and $B$ be 2 points in the plane. Show that if $M$ is the midpoint of the line segment $\overline {AB}$, then $\vec{OM} = \frac{1}{2} (\vec{OA}+\vec{OB})$ where $O$ is the origin. I think I've got this one. Let $A = (a_1, a_2) => \vec{OA}…
StephanCasey
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Is this the correct way to prove by induction?

Prove by induction that $$1 + 3 + 5 + 7 + ... + (2n + 1) = (n+ 1)^2 $$ //for every n ∈ $\mathbb N$. $$1+2+3+...+n=\frac{n(n+1)}2$$ Proof: $$3+5+7+\ldots+(2n+1)=$$ $$=1+2+3+4+5+\ldots+(2n+1)+(2n+2)-1-2(1+2+3+\ldots+…
Bloer
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Prove that the set of equivalence classes is $P$.

Given: Let $P$ be a partition of the set $S$. Let $a$ and $b$ in $S$. Relation $R$ on $S$: $a R b$ iff $a \in X$ and $b \in X$ for some $X \in P$. Then, $R$ is an equivalence relation. I have asked this before, but I am not confident I understood…
El-P
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Prove this function is a bijection

Prove the function $f:\mathbb R \setminus\{0\} \to\mathbb R \setminus \{0\} : x \mapsto \frac1 x$ is a bijection. Surjective? Let y ∈ ℝ ∖ {0} such that y = 1 / x. Notice $f(1/y) = 1 / x = y$. ∴ Surjective. Injective? Test if $f(x_1) = (fx_2)$,…
Jennifer
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How can I prove that $a^n + b$ is composite?

I need to know how could I prove that $2^{33} + 1$ is composite. Thanks!
Ben
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