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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 .

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Proving $a^2$ is even $\implies$ $a$ is even by contradiction

Prove $a^2$ is even $\implies$ $a$ is even. It was proven via contradiction by my friend. Here is the proof in question, which uses proof by contradiction Assume towards a contradiction that $a$ is odd. Let $a = 2k+1$, then $a^2 = 4k^2 + 4k + 1 =…
Jason
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Clarification on properties of division

I'm learning proof by induction and I understand the property that if $p|a$ and $p|b$ then $p|(a+b)$ Can someone elucidate why the following is always true (I'm assuming it's an extension of the property above): In the below equation $a_1,a_2,k,l$…
ClownInTheMoon
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Is this a valid proof for First Principle of Mathematical Induction?

First Principle of Mathematical Induction Let S be a set of integers containing a. Suppose S has the property that whenever some integer $n \ge a$ belongs to S, then the integer $n+1$ also belongs to S. Then, S contains every integer greater than or…
user3000482
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Find an incorrect step in a proof involving the elements of a total order

Theorem: Suppose $R$ is a total order on $A$ and $B \subseteq A$. Then every element of $B$ is either the smallest element of $B$ or the largest element of $B$. "Proof": Suppose $b \in B$. Let $x$ be an arbitrary element of $B$. Since $R$ is a total…
pseudomarvin
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Please check if my reasoning for proof is legal or not

If I have proved a theorem $A$ on the basis of fact $B$, then, is it valid to prove $B$ by using the theorem $A$?
CandidFlakes
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Show that in the factor group $\Bbb Q / \Bbb Z$, there is an element for every $n \in \Bbb N_+$ such that the order of that element is $n$

Task: Show that in the factor group $\Bbb Q / \Bbb Z$, there is an element for every $n \in \Bbb N_+$ such that the order of that element is $n$. Solution: We take a look at the residue class $[$$1 \over n$$]$. It is $n$ $[$$1 \over n$$]$ = $[$$n…
Julian
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Is this proof about a strange isomorphism correct?

Let $X$ and $Y$ be arbitrary sets and $f:X\rightarrow Y$ an isomorphism. Prove that there exist a transformation $g:Y\rightarrow X$ such that $f\circ g$ is the identity in $Y$. As X and Y havn't a structure to preserve, $f$ is just a bijective…
José Osorio
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Is this a valid existence proof for: "there exists a unique real number solution to the equation $x^3 + x^2 - 1 = 0$ between $x = 2/3$ and $x = 1$"

I was wondering if this was a valid existence proof for the following: "there exists a unique real number solution to the equation $x^3 + x^2 - 1 = 0$ between $x = 2/3$ and $x = 1$" Proof: Assume to the contrary that there are two real number…
PutsandCalls
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Confusion on the definition of ∩i∈I Ai

Having a hard time with this one. As I understand it ∩F equals $$\{ x: ∀A ∈ F, x ∈ A)\}$$ which is also equivalent to $\underset{i\in I}{∩} A_i$. And this would mean if F were {{1,2,4},{4,7,8}} then the resulting set of all x ∈ $\underset{i\in…
maybedave
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Prove finite nonempty set of real numbers has a largest element

Prove with induction that every finite nonempty set of real numbers has a largest element. My idea (please fix my notation where it is wrong) Let $A=\left\{a_i\in \mathbb{R}:i\in N)\right\}$. If $i = 1, $ then we conclude that $a_1$ is the…
ALEXANDER
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Need help with this proof ∀x ∈ R[∃y ∈ R(x + y = yx) ↔ x ≠ 1]

Having a hard time proving this one. I can prove this with a contradiction in the (→) direction but I'm stuck on how to prove this in the (←) direction where x ≠ 1 is the given and ∀x ∈ R[∃y ∈ R(x + y = yx)] is the goal. Any help is MUCH…
maybedave
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Interior of a cone is a cone?

I've read somewhere that the interior of a cone is once again a cone. By cone I mean a set $S$ with the property that $(\forall x \in S)(\forall \lambda \geq 0)\ \lambda x \in S$. However, if we consider the cone $C=[0,\infty\rangle$, then its…
implicati0n
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Sequence of fractions which converge to √2

I am a math aficionado and would like to know how to prove that the following sequence of fractions converge to √2 . 1/1; 3/2; 7/5; 17/12; ... In general a(n)=a(n-1)+a(n-2) and a(n+1)=a(n-1)+2a(n-2) Thanks in advance for your help! Matt
user330671
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Prove that the set of natural numbers intersect the set of integers numbers is equal with the set of natural numbers.

We know that the set of natural numbers is a subset of the integer numbers so the common elements of the sets are natural numbers that proves the set of natural numbers intersect with the set of integers numbers is equal to the set of natural…
Anna
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