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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1 answer
$2^n=7x^2+y^2$ solutions
My problem is related to the equation from above. It actually is a very particular one. I noticed that for every positive integer $n$ there's ONE SINGLE solution $(x_1,y_1)$ so that $x_1$ and $y_1$ are ODD positive integers ( I didn't prove it, I…
Anonymus
- 571
2
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2 answers
How do variables work in this proof?
How does this proof work?
Theorem.$\quad$Let $G$ be a group. Then $G$ has a unique identity.
Proof.$\quad$Assume that $e$ and $f$ are two identities in $G$. Since $e$ is
an identity, $ef=f$; and since $f$ is an identity, $ef=e$. Thus $e=ef=f$. …
user372009
2
votes
3 answers
Proof by well ordering: Every positive integer greater than one can be factored as a product of primes.
I am reading the book Mathematics for Computer Science and have reached the chapter 2.3 Factoring into Primes where there is an explanation how Well Ordering can be used to prove the following:
Theorem 2.3.1. Every positive integer greater than one…
Dalibor Čarapić
- 193
2
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2 answers
How to understand case by case decomposition in combinatorics proof
I am just reading through Mathematics for Computer Science (https://courses.csail.mit.edu/6.042/spring17/mcs.pdf) and at chapter 1.7 Proof by Cases there is a following theorem as an example:
Theorem. Every collection of 6 people includes a club of…
Dalibor Čarapić
- 193
2
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1 answer
One step in the derivation of the expectation maximization algorithm.
Although there are some answers to related problems I've found no direct solution to this specific problem.
I'm reading this in depth introduction to the expectation maximization algorithm and got stuck in a step in its derivation.
On page 6 in…
Harald Thomson
- 189
2
votes
1 answer
Showing this number is irrational
Prove the number $\log_2 3$ is irrational
My attempt:
Assume that $\log_2 3 $ is rational
By definition $\log_2 3 =y$
Also by definition $y=\frac{a}{b}$ such that $b \neq 0$
Now you have $ 2^{\frac{a}{b}}=3$
Thus raising both sides by $b$ you…
HighSchool15
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3 answers
Using AM-GM inequality to prove
prove that $$x^4 + y^4 + z^4 \geq xyz(x+y+z)$$
This AM-GM inequalities are seriously stumping me. I'd appreciate a full proof and explanation and hints for proving other inequalities like this. Thanks.
user346756
- 293
2
votes
3 answers
A proof that $0=1$?
I saw a proof in a comment on a previous MSE question yesterday and I can't stop thinking about it. It looked like the following:
$0 = (1-1) + (1-1) + \cdots = 1 + (-1+1) + (-1 + 1) + \cdots = 1 + 0 + 0 + \cdots = 1$
Where does the proof go wrong?…
1
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0 answers
Doubt in a Dzul-Kifli's paper on Devaney chaos
While reading this paper, I came across following argument (in Lemma 5):
Consider the least $k$ such that $f (I_k) = I_j$ and $j < k$. Clearly $k > 1$ and $f(I_{k−1})
= I_m$ for some $m > k − 1$. We consider three cases: (a) $j = k − 1$ and $k =…
Ajin Shaji Jose
- 752
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vote
1 answer
Question on proof for: If $a$, $b$, and $c$ are real numbers with $a<0$, then there is a real number $y$ such that for every real $x$, $ax^2+bx+c≤y$.
I have a very weak background in math and am (slowly) attempting to learn more. I'm starting with "How to Read and Do Proofs" by Daniel Solow (5th edition). In Chapter 7 (pg.83), he presents this proposition:
If a, b, and c are real number with a <…
Nikki_B
- 13
1
vote
0 answers
Methods of mathematical proof's
I have a curiosity about mathematical proofs and I don't know how to research it properly. I apologize to the admins in advance, but it's a genuine question.
Given a proposition P, are there other demonstration methods that allow me to prove that P…
1
vote
1 answer
Let $U_{r}(a)\subset X$. For $x,y\in U_{r}(a)$ there exist a continuous function $f:[0,1]\to X$ such that its image is entirely in $U_{r}(a)$.
Claim:
Let $(X,d)$ be a metric space. Let $U_{r}(a)\subset X$ with $\epsilon >0$ and $a\in X$. For every tow points $x,y\in U_{r}(a)$ there exist a continuous function $f:[0,1]\rightarrow X$ such that $f(0)=x$, $ f(1)=y$ and its image lies entirely…
distortedPicture
- 117
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0 answers
Motivation for the Gauss substitution in the proof of the AGM integral form
I tried to understand the integral form of the AGM and its connection to the complete elliptic integral of first kind. (similar to this question)
The main point is to show that
$$\int_0^{\frac{\pi}{2}} \frac{\mathrm{d}\theta}{\sqrt{x^2 \cos^2 \theta…
mikuszefski
- 111
1
vote
0 answers
Understanding a proof that $\frac{a^m-1}{a-1}=2b^2$ has no solution for $m>2$, and whether the argument can apply to $\frac{a^m-1}{a-1}=\frac{2b^2}c$
In this answer of MO it is showed that $$\frac{a^m-1}{a-1}=2b^2$$ has no solution for $m>2$.
I would like to check if using the same argument, it can be stated that $$\frac{a^m-1}{a-1}=\frac{2b^2}{c}$$
where $c,b$ are odd, has no solution for $m>2$.…
Juan Moreno
- 1,110
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vote
3 answers
Inequality Proof Question is Confusing Because it Contains extra Variables
I am trying to help my daughter with her homework. I am confused by the problem, but I will admit that the math is a bit over my head.
Here is the beginning of the problem:
Let a $\in \mathbb{R}$. Prove that $a^2 \le 1$ if and only if $-1 \le a…
Vaccano
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