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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Prove "If, in a country, there are $x$ fallow acres for every planted acre, yield per planted acre is $1+x$ times the yield per total acre."
If, in a country, there are $x$ fallow acres for every planted acre,
yield per planted acre is $1+x$ times the yield per total acre.
Thus the ratio of yields per planted acre between the Soviet Union (S)
and the U.S. (U), $.68$, is…
user685057
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2 answers
Question about continuity of function in a proof of L'Hospital Theorem
$$f;g:[a,b] \rightarrow R \, \, \forall x \in (a;b) \, \, g'(x) \neq 0,$$ $f,g$ are differentiable in $(a,b)$. If $$\lim_{x \to a} f(x) = \lim_{x \to a }g(x) = 0$$ and there exists a $$\lim_{x \to a} \frac{f'(x)}{g'(x)},$$ then $$\lim_{x \to a}…
user
- 1,412
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Proof by infinite descent
Proof by infinite descent is used, for example, to prove the irrationality of sqrt2. But can it be used also to prove that a property holds true for an infinite set? If so, is there an example?
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Infinite Descent Principle
I am trying to solve Exericse 4.4.2 in Tao's real analyis textbook, but am having some trouble finishing it, and was hoping someone could take a look at what I have. Here is a copy of the exercise.
A definition: a sequence of $a_0, a_1, a_2,…
user465188
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1 answer
Proving the sum of the shaded areas is equal to the incircle (in an equilateral triangle).
I have worked through proving all the basic properties of the triangle, but I am confused about the concluding statement the author makes after this:
‘The relation R = 2r, which is a consequence of the coincidence of the circumcenter (intersection…
Jamminermit
- 1,923
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3 answers
Apostol calculus 2- Legendre polynomials
I'm trying to understand this formula that Apostol uses to define Legendre polynomials.
Suppose $$\alpha=2m, m\in \mathbb{Z}$$ Then:
$$(2m+1)(2m+3)\dotsb(2m+2n-1)=\frac{(2m+2n)!m!}{2^{n}(2m)!(m+n)!}$$
I don't understand the right hand side of this…
SMath
- 369
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2 answers
Tricky proof of inequality
Positive numbers a, b and c are given. How one can prove that
$$a^3 + b^3 + c^3 + ab^2 + bc^2 + ca^2\geq2(a^2b + b^2c + c^2a)$$
Anatol
- 1
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2 answers
A congruency proof question using circles
This is one of the last questions on a test and I couldn’t get the correct answer. The writing in red is my teacher’s, so my question is how would you prove it with the information my teacher has pointed out and is there any way that my original…
Jamminermit
- 1,923
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3 answers
The Division Algorithm
Question: Find integers $q$ and $r$ such that $m = qd + r$, $0$ $\leq$ $r$ $<$ $d$.
Given: $m = -2$, $d = 5$.
This is what I have so far:
$-2 = 5q +r$
Dividing $2$ into $5$ gives $q = 2$ and $ r = 1$
So, then
$-2 = 5(2) + 1$
Because $-m$ is…
KM9
- 135
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1 answer
Is it possible that I find a number from 2 informations then I try of the number work and it dosent?
Imagine I got 2 conditions or informations to find a unknown number x and did many steps ( of course mathematically correct with no mistake) using both conditions to find a value of x. Is it possible, to replace x and see it not work for any…
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3 answers
Why is can number be divided by 3(ofc I mean we get an integer result) if its sum of digits can be divided by 3
Why is can number be divided by 3(ofc I mean we get an integer result) if its sum of digits can be divided by 3?
Please post an easy proof since Im in grade 9:)
I know there are already proofs but can someone show me a proof for the level of a grade…
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Is this proof convincing for substitution as a grade 9 student?
Consider the system:
$$
ax+by=c \qquad (1)
$$
$$
a'x+b'y=c' \qquad (2)
$$
For $x$ to be a solution of equation $(1)$, it has to respect the relation $x=(c-by)/a$. We substitute this value of $x$ into the second equation for it to to be solution of…
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Explaining the Result of an Equation
Let $Y$ be a closed subset of a Hilbert space $H$. Let $x \in H, z \in Y$. This equation comes from a proof in Lax' functional analysis book, and the other parts of the proof are not relevant:
$$
2tRe() + t^2||z||^2 \geq 0,
$$
where $ $…
A Slow Learner
- 1,201
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Elementary Proof: Let $x$ be an integer. If $4|x^2$, then $4|x$
All I have so far is pretty much the definition:
$x^2=4a$
Doing the square root doesn't seem to help, so I thought about using the contrapositive approach, but how would you say that $x$ doesn't divide $4$, definition-wise? Something with…
lortick
- 45
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1 answer
Newbie confusion on introduction to proofs.
My problem: Show that if $3$ is a factor of $2n$ then $3$ is also a factor of $n$.
Solution: If $3$ is a factor of $2n$ then some integer constant $k$ exist such that $3k=2n$. Now, $2n$ is even hence $3k$ is even and $k$ is even and so $k$ is…
CountDOOKU
- 1,065