Mathematics Stack Exchange
Mathematics Stack Exchange

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
18
votes
3 answers

False Proof that $\sqrt{4}$ is Irrational

Everyone with any basic knowledge of number theory knows the classic proof of the irrationality of $\sqrt{2}$. Curious about generalizations using elementary methods, I looked up the irrationality of $\sqrt{3}$, and found the following: Say $…
Brevan Ellefsen
  • 14,793
17
votes
2 answers

Showing a linear map is injective if and only if kernel is {$ {0} $}

So my prof gave me this proof: $f(x) = f(y) ⇐⇒ f(y − x) = 0 ⇐⇒ y − x ∈ Ker f.$ I dont see why this proof is enough, this only says $y-x \in Ker f$
asddf
  • 1,733
9
votes
3 answers

Verifying This Proof for Alternating Harmonic Series

Using the fact that $$2^n=\sum^n_{k=0}\binom{n}{k}$$, we can generalize this sum and say that $$2^n=1+n+\frac{n(n-1)}{2!}+\frac{n(n-1)(n-2)}{3!} +...$$such that $n \in \Bbb Z, n \ge0$ Now notice how the constant in the last factor of each term is…
Badr B
  • 631
  • 5
  • 13
9
votes
1 answer

Is this a correct proof?

For every $r,s \in \mathbb{Q}$ with $r
Max
  • 1,275
9
votes
1 answer

Prove that square of even integer is even.

Is my proof correct? Suppose $n=2m$ is an even integer. Since $n=2m$ , then $n^{2}=(2m)^{2}$ $n^{2}$ = $(2m)^{2}$ = $4m^{2}$ =$2(2m^{2)}$ Since $(2m^{2})$ is an integer and $2(2m^{2})$ is in the form $2m$ , we have proven that the…
Curious_guy1111
  • 271
8
votes
3 answers

Is this a valid proof that A = B given A ∩ B = A ∪ B?

Here is my proof. My instructor claims that it is invalid because I did not use a set membership table, and that the use of a predicate logic truth table is invalid. That makes no sense to me. If I can do S := { x | P(x) }, then I should obviously…
okovko
  • 201
7
votes
4 answers

Proof: $n^2 - 2$ is not divisible by 4

I tried to prove that $n^2 - 2$ is not divisible by 4 via proof by contradiction. Does this look right? Suppose $n^2 - 2$ is divisible by $4$. Then: $n^2 - 2 = 4g$, $g \in \mathbb{Z}$. $n^2 = 4g + 2$. Consider the case where $n$ is even. $(2x)^2 =…
Daniel
  • 189
6
votes
4 answers

if $a$ and $b$ are irrational and $a \neq b$, then is $ab$ necessarily irrational?

$\sqrt{2}\sqrt{2}$ is rational so it is not the case $\forall$ m,n $\in$ $\Bbb{R} - \Bbb{Q}$ , mn $\in$ $\Bbb{R} - \Bbb{Q}$. What about if m $\neq$ n? Is there a case where m $\neq$ n and $mn$ is rational?
Anthony O
  • 363
6
votes
3 answers

How to improve my proof that $\{n \in\mathbb{Z}|\exists k \in \mathbb{Z}|n=4k+1\}= \{n \in \mathbb{Z}|\exists j \in \mathbb{Z}|n=4j-7\}$?

I am not cheating my homework. This was already handed in, and handed back with a grade. I'm not sure if my teacher is a harsh grader, or if I really am doing as bad as she makes it out to be. I figured a few people here might be able to help me get…
Michael Rector
  • 127
6
votes
3 answers

Why do we need to prove a fraction can always be written in lowest terms?

I'm currently reading the notes of a preliminary Math course. Section 3.1.1 contains some proofs using the Well Ordering Principle. One of them is about the always apparent possibility to write a fraction in shortest terms. But why does this require…
cadaniluk
  • 217
6
votes
5 answers

Prove that the sum of the squares of two odd integers cannot be the square of an integer.

Prove that the sum of the squares of two odd integers cannot be the square of an integer. My method: Assume to the contrary that the sum of the squares of two odd integers can be the square of an integer. Suppose that $x, y, z \in \mathbb{Z}$ such…
Matt
  • 297
6
votes
4 answers

$\sqrt{2}$ cannot represent a rational number

I am not asking for a proof that shows me that $\sqrt{2}$ cannot represent a rational number, because I have already seen one by contradiction, which was quite simple, but I have problems in understanding the following proof: By Rational Zeros…
user168764
5
votes
4 answers

$\lim\limits_{n \to \infty}\frac{n^{\alpha}}{c^n}=0.(\alpha>0,c>1)$

Problem Assume that $\alpha>0,c>1.$ Prove $$\lim_{n \to \infty}\frac{n^{\alpha}}{c^n}=0.$$ Proof Denote $b=c^{\frac{1}{\alpha}}$. Then $$\frac{n^{\alpha}}{c^n}=\frac{n^{\alpha}}{(b^{\alpha})^n}=\left(\frac{n}{b^n}\right)^{\alpha}.$$ Notice that…
mengdie1982
  • 13,840
  • 1
  • 14
  • 39
5
votes
5 answers

Prove $\lim\limits_{n \to \infty}\frac{a^n}{n!}=0~~~(a>0).$

Problem Prove $$\lim_{n \to \infty}\frac{a^n}{n!}=0~~~(a>0).$$ Proof Denote $x_n=\dfrac{a^n}{n!}$ where $n=1,2,\cdots.$Then $$\frac{x_{n+1}}{x_n}=\frac{a^{n+1}}{(n+1)!}\cdot \frac{n!}{a^n}=\frac{a}{n+1}\to 0~~~(n \to \infty)$$which implies the…
mengdie1982
  • 13,840
  • 1
  • 14
  • 39
5
votes
2 answers

Proving, by contradiction, that there are infinitely $n \in \mathbb{Z^+}$ such that $\sqrt{n}$ is irrational.

I would like to know whether I have proved this statement correctly using contradiction and if not get some tips or pointers on how to improve it/make it correct. We are asked to prove that there are infinitely $n \in \mathbb{Z^+}$ such that …
Cro-Magnon
  • 885
1
2 3
…
36 37