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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On the density of $\mathbb{Q}$ in $\overline{\mathbb{R}}$.
We know that if $x,y\in\mathbb{R}$, $x
Jack J.
- 920
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4 answers
Prove the contrapositive of "if $x + y + z$ is odd, then at least one of $x, y$, and $z$ is odd",
I want to prove the contrapositive of this: if $x + y + z$ is odd, then at least one of $x, y$, and $z$ is odd.
I think the contrapositive is this: if at least one of $x, y$, and $z$ is even, then $x + y + z $ is even.
For the proof I'm not sure;…
isthewiz
- 51
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2 answers
Proving |sinx| =< |x| for all real x.
Everything I did to solve this problem matches the book, except for the last bit.
Use the following to verify the statement $|\sin x| \leq |x|$.
a) Show that for all $x \geq 0$, $f(x)=x-\sin x$ is non-decreasing.
$f'(x) = 1-\cos x$. Since $-1 \leq…
mXdX
- 571
- 3
- 14
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1 answer
A short question related to the proof of inverse function theorem in Rudin's PMA (9.24)
This is the theorem:
9.24 Theorem Suppose $f$ is a continuously differentiable map of an open set $E
\subseteq \mathbb{R}^n$ into $\mathbb{R}^n$, $f'(a)$ is invertible for
some $a \in E$ and $b= f(a)$. Then
(a) There exists open sets $U,V$ in…
Sakamoto-I
- 55
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2 answers
Proof by induction, inductive step problem
Prove by induction:
$$\sum_{i=0}^n 3^i =\frac {1}{2} (3^{n+1}-1)$$
Now, i know how to do the first step and i understand it but then i have a problem with the second step which is showing that its true for n+1.
My question is:
Is this notation…
mBart
- 13
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1 answer
Given a function a to b, its inverse relation will be a function iff the function is bijective
So when I did this proof I didn't know I was supposed to physical prove all the parts out (assuming they are both functions and then using that to prove the inverse is an injection). My problem is I have never seen a relation proof using a function…
George
- 117
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2 answers
Why are backwards arguments not ok
When you are given information and asked to show 'something' is it completely wrong to start with that 'something' and work back to the information?
Can you start with what you want to show, work backwards a few steps using equivalence and then show…
Carlos Bacca
- 638
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0 answers
Proof for set of 15 values that have property a−c=d−b
I am pretty sure (please correct me if this is untrue), that in a set of 15 different values, ranging from integers (1-100), that there are four numbers, a,b,c,d such that a−c=d−b.
I have tried to understand why this is true, but just cannot wrap my…
SweetChilli
- 31
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1 answer
Euclid Lemma proof reasoning
This question is more concerned with understanding the reasoning behind mathematical proving rather than explaining this specific proof. I understand why this proof works.
This is the proof of Euclid Lemma from Wikipedia:
This
states that if…
Michael Munta
- 175
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1 answer
For every $n\in \Bbb{N}$, either $n$ is even or $n-1$ is even (Must use Induction)
I have gotten a lot of the proof done so far but I am now stuck: Pf: Let $n\in\Bbb{N}$. $P(n)$ is the statement, "$n$ is even or $n-1$ is even"
Base Case ($n=1$): $n=1$ and $1-1=1$ so $n-1$ is even. $P(2)$ holds.
Induction: Let $k\in\Bbb{N}$. We…
user593509
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1 answer
Proof: identitiy of $f_1(t)$, $f_2(t)$ for $t\in(0,1)$
During solving some spherical problem by 2 independent ways I found "two" solutions represented by $f(t)$
$$f_1(t)=\frac{\sqrt{1+t}(2-t)}{t(\sqrt{1+t}-\sqrt{1-t)}},$$
and
$$f_2(t)…
justik
- 383
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1 answer
Trouble understanding a step in a proof, algebra with summation
I have this line in a proof that I do not understand and would like some help understanding please.
$$\sum_{i=1}^{n}x_i^2-n\bar{x}^2 = \sum_{i=1}^{n}(x_i^2-2x_i\bar{x}+\bar{x}^2)$$
Can anybody enlighten me on this transformation please?
Thanks.
Bucephalus
- 1,386
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1 answer
A function $ f : [0,1] \to \Bbb{C} $ is differentiable with derivative 0, is constant.
In Conway's complex analysis while proving proposition 2.10
"If $G$ is an open connected set and $ f : G \to \Bbb{C} $ such that $f'(z)=0 \ \forall z \in G$ then f is constant"
He fixes some $z_{0} \in G$ and defines the set $A=$ {$z \in G:…
Uday Khanna
- 309
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1 answer
Proof by well ordering: Every positive integer greater than one can be factored as a product of primes. Part II
I have a question related to the one found here. I am struggling to understand this part of the proof:
So $n$ must be a product of two integers $a$ and $b$ where $1 < a, b < n$. Since $a$ and $b$ are smaller than the smallest element in $C$
How…
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1 answer
Is this proven by the generalized De Morgan's laws for propositional connectives?
I know the generalized De Morgan's laws say
$\begin{align*}
\neg[P(0) \wedge P(1) \wedge \ldots \wedge P(n)] \Leftrightarrow \neg P(0) \vee \neg P(1) \vee \ldots \vee \neg P(n)
\end{align*}$
for any finite $n$. And I can prove the above by…
user279420