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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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$\Bbb Q$ is dense in $\Bbb R$

I tried a proof using mainly the Archimedean property of $\Bbb R$: I am to show that for any $x\in \Bbb R$, every neighborhood of $x$ contains a rational number. I shall first prove it for non-negative real numbers. Suppose $x$ is a non-negative…
Not Euler
  • 3,079
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1 answer

Where I'm going wrong?

Find the value range of $p$ if interval $(1,2)$ lies between the roots of $$2^x + 2^{2-x} + p = 0.$$ The answer is $(-\infty,-5)$. My ''solution'': Let $t= 2^x$, so $t \in(2,4)=:I$. Now you can write $$f(t) = -t-{4\over t}$$ Clearly since…
nonuser
  • 90,026
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3 answers

Limit proof using epsilon-delta

So I need to prove $$\lim_{x \to 2} \frac{2x^2-3x-2}{x^2-5x+6}.$$ Here's what I did: $$\left|\frac{2x+1}{x-3} + 5\right| = \left|\frac{7(x-2)}{x-3}\right| < 7\delta\left|\frac{1}{x-3}\right|,$$ and now I am stuck; normally we will further restrict…
HD5450
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How can one prove that $\sqrt{ 2} \cdot \sqrt{ 3} = \sqrt{ 6}$?

I have already proved that $\sqrt{2}\cdot \sqrt{2}=2$ so I hope I can now use $\sqrt{3}\cdot \sqrt{3}=3$ and the same for 6. The exercise comes from Stillwell: Mathematics and its History. The other exercises have not been complicated so probably…
Kang
  • 137
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2 answers

Minimum of $xy+yz+xz=k$

Given that the sum of x,y,z is 3 find the minimum of xy from the relation$$xy+yz+xz=k$$ Is there anything wrong with my solution since someone said the correct answer differs?…
user556151
2
votes
1 answer

Solving Trig equations: tan 2x + tan x - 2 = 0

How to solve tan 2x + (tan (x)) - 2 = 0? I already rewrote tan 2x in its double angle identity format, but I don't know where to go from there, or if I'm even doing it right.
shhh
  • 35
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4 answers

Prove any odd square cannot be of the form $4n+3$

This is both a problem, and an opportunity for me to learn proof building, so sorry for being too detailed. An 'odd square number' means : a square number which is odd also, e.g. $9, 25, 49, 121, 169$. Square of an odd number (which can be of the…
jiten
  • 4,524
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1 answer

Trying to construct hyperreal numbers from functions

This is a line of thought about an algebraic approach to infinity I've been on and off since I was young. This is the closest I've come to deriving this "number" (?) $\omega$ in a logical way (I believe it's a different object to Cantor's $\omega$…
Supware
  • 940
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If $H\unlhd A_n$ has a 3-cycle, then $H=A_n$

Let $H$ be a normal subgroup of the alternating group $A_n$ ($n\geq5$) such that the 3-cycle $(i j k)\in H$. Then, $H=A_n$. I think this proof is wrong because I can't see where the hypothesis $n\geq5$ is used. Proof: I will use two facts: first, if…
Veridian Dynamics
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Product of cyclic groups is cyclic iff their orders are coprime

Let $G=(g^i)_{i\in\mathbb{N}},\ H=(h^i)_{i\in\mathbb{N}}$ be finite cyclic groups such that $(g,h)$ generates $G\times H$. I want to prove that $\gcd(|g|,|h|)=1$ (where $|g|=|G|$,etc) Let $k\in\mathbb{Z}$ such that $(g,h)^k=(g,h^2)$. Then,…
Veridian Dynamics
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Prove that if $T(n) = T(n - 2) + n^2$ then $T(n) = O(n^3)$ as $n\to\infty$

I am studying for an exam, and one practice problem I attempted asks me to prove that: $T(n) = T(n - 2) + n^2 = O(n^3)$ I need to use the induction/substitution method for this problem. My proof attempt is below. Is this correct? If so, is there a…
Daniel
  • 189
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1 answer

Why is this proof false? $\sqrt 2 + \sqrt 6 < \sqrt 15$

What is wrong with the given proof? $$ \sqrt 2 + \sqrt 6 < \sqrt 15 \\ (\sqrt 2 + \sqrt 6)^2 < 15 \\ 2 + 6 + 2\sqrt2\sqrt6 < 15 \\ 2\sqrt2\sqrt6 < 7\\ 2^2 \cdot 2 \cdot 6 < 49 \\ 48 < 49 $$
Viper
  • 49
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2 answers

How to prove that there is a unique positive real number $x$ such that $x^2 = 2$?

How to prove that there is a unique positive real number $x$ such that $x^2 = 2$? My step: suppose there are $2$ positive real number $x, y$ such that $x^2=y^2=2$, then we take sqrt of both and we get $\sqrt{x^2}=x=y=\sqrt{y^2}$. Is it right?
CoolKid
  • 2,738
2
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2 answers

Is my reasoning correct (regarding minimal distance on graph)

Question: Given two point $A(0,10)$ and $B(30,20)$, find the point $P$ on x axis for which sum of distances from given points to the required point is minimum Now i could form a lengthy equation and use differentiation but instead I decided to…
Anvit
  • 3,379
2
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0 answers

Any idea for solving an equation of the type: $(t^a+x)^{1/a}=(t^b+x)^{1/b}$?

I am trying to solve this equation: $$(t^{\beta_X}-log(1-p))^{1/\beta_X}=(t^{\beta_Y}-log(1-p))^{1/\beta_Y},$$ where $t,\beta_X,\beta_Y>0$, $p\in(0,1)$. I know that there is a solution under some conditions as you can see…
user3149230
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