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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Proof Critique: For any $b\in \mathbf{N}$, $b++$ is unique.
As I was trying to answer this question (using only the peano axioms), I came up with the following "proof". On a second look, I noticed a flaw. But I'm struggling to articulate why or what the flaw is. Could somebody take a look, and let me know if…
skm
- 81
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1 answer
question on proving the compositions o functions is associative
Simple question but what is the definition that allows me to take (assume everything that is also needed for this proof is here) $(f \circ g) \circ h(w)$ and turn it into $f(g(h(w)))?$
I see this used a lot in function proofs, but I'm not sure…
George
- 117
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5 answers
How to proof the reason?
I have this statement:
If $\frac{a}{b} = \frac{c}{d},$ prove that
$\frac{a+b}{a-b}=\frac{c+d}{c-d}$
I tried to add 1, multiply 1 and nothing.
My development was:
$\frac{a}{b} - \frac{b}{b} = \frac{c}{d} - \frac{d}{d}$
$\frac{a-b}{b} =…
ESCM
- 3,161
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Similarity between sum of probabilities and Grassman formula
I don't know if this has been covered before, or if there's even anything to say about this.
On the first hand, given to events $A,B$ with probability $P(A),P(B)$, we can prove from the axioms of probability that (for events not necessarily…
TeicDaun
- 202
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Prove that $f(x) = x ^ {2n+1}$ is injective.
So I need to prove that
$$f : \Bbb R \rightarrow \Bbb R,\quad f(x) = x ^{2n+1},$$
where $n\in\Bbb N$ is an injective function. Or rather I need to prove that the function of a number to an odd exponent is injective.
I've been trying to prove it…
Relikus
- 29
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2 answers
Why is the product of both numbers always an integer root?
I have two numbers. $x, p$
This numbers, have a integer root, then:
$\sqrt{x} \in \mathbb Z, \sqrt{p} \in \mathbb Z$. And also:
$x = c^2$, $p = d^2$, because it have a integer root.
So, prove that $xp = k$, where $k$ have a integer root.
My…
ESCM
- 3,161
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2 answers
Proving sum of even + odd = odd in the opposite direction.
Every child knows this proof:
Assuming that:
$odd(x) = 2a + 1$, where $a \in \mathbb{N} $ and
$even(y) = 2b + 1$, where $b \in \mathbb{N} $ and also
$\lnot odd(x) = even (x)$
$\lnot even(x) = odd (x)$
then: $odd(x) \land even(y) \rightarrow odd (x +…
R. Rengold
- 125
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1 answer
For $x \in \mathbb{R}$, if $x$ is irrational then $\sqrt[3]{x}$ is irrational.
Getting caught up on this problem. what i got so far.
Contrapositive: For $x \in \mathbb{R}$, if $\sqrt[3]{x}$ is rational, then $x$ is rational.
If $\sqrt[3]{x}$ is rational then there must exist an $a,b \in Z, b \neq 0$ such that…
Ringomain
- 91
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1 answer
Canola Oil problem
A retailer purchased 38 gallons of canola oil and wants to put the oil in smaller cans (all of the same size) for sale. He knows his customers will NOT be interested in buying less than 3/5 of a gallon or more than 4/5 of a gallon of oil at a…
user536513
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1 answer
Problem understanding the proof of the principle of virtual work
I'm having some trouble understanding the proof of the Principle of Virtual Work for deformable bodies. I'll give below the proof that I've read, and, next, I'll remark what I'm not understanding. I asked this question on Physics and Engineering…
muimerp
- 75
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0 answers
Evan's proof of approximation by smooth functions up to the boundary of Sobolev functions
My question: Why is the function $f_\epsilon$ continuous (smooth) up to the boundary?
This is theorem 4.3 in the new edition of Evans & Gariepy's "Measure Theory and Fine Properties of functions."
I understand the proof and constructions. However I…
Behnam Esmayli
- 5,024
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1 answer
Why does it follow?
In this proof, I am trying to understand why "It follows that $w\in\mathbb{R}$ and that $w$ can be expressed as $\sup\left\{a_{r}\mid r\in\left(0,\frac{\epsilon}{2}\right)\right\}$." So here are my questions:
Here,…
user281997
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1 answer
Proving $P$ for $N(n+N-1)$
Let $n$ be a non zero natural number.
We say that $n$ has the property $P$ if there exists a sequence of numbers $a_k$,$a_1$,$a_2$...$a_m$ strictly positive rational numbers (not necessarily distinct), we get : $\sum_{k=1}^m a_k$ $=$ $n$ and…
Mario SOUPER
- 149
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Proof explanation required
Could someone explain or comment the proof X from my lecture notes?
We have been given:
$A \in \mathbb{C}^{m \times n}$
$A^+$ a Moore-Penrose-Inverse
$V$ some unitary space
$b \in \mathbb{C}^m$
a system of linear equations $Ax=b$
the theorem Y…
jupiter_jazz
- 517
1
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3 answers
Factoring within a proof
In the proof text I am using, I am trying to understand a proof of the fact that the geometric mean is less than or equal to the arithmetic mean by showing that:
rst $\le$ (r$^3$ + s$^3$ + t$^3$)/3
The answer in the back says to note that:
r$^3$ +…
cdm2003
- 13