For posts seeking explanation or clarification of a specific step in a proof. "Please explain this proof" is off topic (too broad, missing context). Instead, the question must identify precisely which step in the proof requires explanation, and why so. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplicate questions.
Questions tagged [proof-explanation]
11824 questions
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Monotone class theorem - proof explanation
I am studying the proof of the monotone class theorem in the book "Real analysis for graduate students" by Richard Bass, but I got stuck at a particular point.
The idea behind the proof is clear to me, we want to define subsets ($\mathcal{N}_i)$ of…
UpzYaDead
- 107
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1 answer
Proof of one of the most beautiful equations in Math.
$\cfrac{1}{1^2} + \cfrac{1}{2^2} + \cfrac{1}{3^2} + ...... \infty = \cfrac{{\pi}^2}{6}$
Often termed as one of the most beautiful equations in math:
I tried devising a proof for the above formula.
But I got stuck just as soon as I begun. Addition of…
user880107
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1 answer
(2n + 1) + (2n) is odd?
I'm looking at basic proofs in Lang and in Downing. Here's the proof in question in Downing:
$m$ and $n$ are natural numbers $\ne 0$.
$$s = (2n) + (2m + 1)$$
$$s = 2(m + n) + 1$$
Thus the answer is odd by an earlier definition of odd as $2n +…
Beegs
- 25
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2 answers
How to approach proof of "For an integer n, if $n > 7$, then $n^2-8n+12$ is composite"?
For the first part of this question, I was asked to find the either/or version and the contrapositive of this statement, which I found as follows:
i) either $n \leq 7$, or $n^2-8n+12$ is composite
ii) if $n^2-8n+12$ is not composite, then $n \leq…
lswift
- 67
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2 answers
Theorem 2.41 in Baby Rudin
I am reading Theorem 2.41 in Baby Rudin. Rudin proves that in $R^n$ every infinite subset $E$ has a limit point of $E$ implies that $E$ is closed. I understand what he wants to do. For references his proof is here:
2.41 $\ \ $ Theorem $\ \ $ If a…
user651166
- 63
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More about Darboux theorem
Can you explain the differences or relationships between Darboux theorem and Riemann Integral? I thought that Darboux theorem was about derivative but why internet connects this with integral? It does not have to be so profound.. Please help me.…
TCLee
- 37
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Unknown Variable ‘$L$’ encountered in equation
I was going through S.L. Loney’s Plane Trigonometry-Part 1.
I encountered this equation over here :
$$ \sin{B} = \frac{b}{c}$$
Where $B$ is an angle of a Triangle $ABC$, $b$ and $c$ respective sides opposite to angles $B$ and $C$. ($c$ - hypotenuse…
Vulcan
- 11
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1 answer
Is the statement "$a^2 = b$ and $b > 0$, then $a=\sqrt{b}$" true or false?
I am trying to determine the truth value of the proposition "If $a^2 = b$ and $b > 0$, then $a=\sqrt{b}$.".
Based on the answer of my teacher, the truth value statement is false.
The counterexample is when $a=-\sqrt{b}$.
My answer is that the truth…
AYA
- 578
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How can this condition of concurrency of three lines be understood?
I saw the answer to the same doubt I had the other day but can anyone please explain it to me more simply?
Let there be three lines given by the equations:
$$
\begin{cases}
a_1x+b_1y+c_1=0 \\
a_2x+b_2y+c_2=0\\
a_3x+b_3y+c_3=0\\
\end{cases}
$$
Now, a…
Jay Agarwal
- 11
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1 answer
Adams Sobolev Space: Lemma 2.27
Let $0\le r\le 1$ fixed and $0\le \theta< 2\pi$. Let $1
Jack J.
- 920
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1 answer
Contrapositive Proof to show that for $x,y ∈ ℤ$, if $5∤xy$, then $5∤x$ and $5∤y$
I need to use a contrapositive proof to show that for $x,y ∈ ℤ$, if $5∤xy$, then $5∤x$ and $5∤y$.
So far I've got that the contrapositive statement would be "if $5|xy$, then $5|x$ and $5|y$". Obviously this is not true as $2*5=10$, 10 and 5 being…
gigaman76543
- 11
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1 answer
problem understanding Systems of distinct representatives
I have been given the problem
"Let P={S_1,S_2,...,S_r} be a family of distinct nonempty subsets of the set {1,2,...,n}. If the S_i are all of the same cardinality (|S_i|=k), then prove that there exists an System of Distinct Representatives (SDR)…
user2912093
- 11
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3 answers
How to prove $xy>x+y$ if $x,y \in (2,\infty)\subseteq \Bbb R$
I am new to proofs. This is my first proof-based mathematics class, and it is a hard transition from my high school classes. I am a second semester freshman.
My original question was:
Prove that there is a real number with the property that for any…
Kenneth Dang
- 117
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1 answer
"For all" versus "There exists"
My class uses the book "The Art of Proof" by Matthias Beck and Ross Geoghegan. Proposition 1.12 states:
Let $x\in\mathbb{Z}$. If $x$ has the property that for each integer $m$, $m+x=m$, then $x=0$.
The proof isn't shown in the book, but the proof…
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1 answer
Explanation to a proof of: $f\left(x_0+\frac{\tau}{2}\right)=f(x_0)$ for some $x_0\in\mathbb R$
The problem has already been solved by a user who deleted his account so I ask a question regarding his answer.
This was the posted problem:
Let $f:\Bbb R\to\Bbb R$ be continuous & periodic with prime period $\tau>0$. Prove: $\exists x_0\in\Bbb R$…
PinkyWay
- 4,565