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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Handling long inequalities on short width paper
I have a long inequality in a single line
$(1+a)^{k+1}=(1+a)^k(1+a)\ge(1+ka)(1+a)=1+(k+1)a+ka^2\ge 1+(k+1)a$
But I find it difficult to show when the width of my paper is short. What can I do to make the lines readable for short width papers.
Veak
- 177
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How to derive the formula for present values and future values of constant cash flow at fixed interest rate?
I'm not sure how can the following formula be derived. Please explain step by step with reasons:
Present value of constant cashflow at fixed rate:
Future value of constant cashflow at fixed rate:
Student
- 131
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2 answers
Overlapping vs. Continuous hotel bookings
A colleague and I are trying to figure out if the following statement is true and if so, which mathematical theorem and formulations are the one that apply here:
Given a hotel with N rooms of the same type.
If for every day of a proposed reservation…
Khepin
- 101
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Suppose $A$, $B$, and $C$ are sets, $A \backslash B ⊆ C$, and $x$ is an arbitrary object. Prove that if $x\in A\backslash C$ then $x ∈ B$
Suppose $x \in A \backslash C$. This means that $x \in A$ and $x \notin C$. Suppose $x \notin B$.
Then $x \in A \backslash B$, so since $A \backslash B ⊆ C$, $x \in C$. But this contradicts the fact that
$x \notin C$. Therefore $x ∈ B$. Thus, if $x…
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Explain Arrow's Impossibility Theorem
Wikipedia claims for the proof of Arrow's Impossibility Theorem that when
Every voter in segment one ranks B above C and C above A.
Pivotal voter ranks B above A and A above C.
Every voter in segment two ranks A above B and B above C.
(B and C may…
Number Basher
- 292
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Why must there be a sequence which converges to (m,b) if they are the arguments of a continuous function, but not a local maximum?
I have been reading the paper "Monty Hall game: a host with limited budget" and trying to follow the arguments the authors make. However, I have been struggling to understand what they outline as Lemma 4.1.
In particular, they state:
If $g(m,b) =…
Joe McKeown
- 51
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I'm new to proofs, does anybody have a proof that three times a prime is always greater than the next consecutive prime?
Numbering the primes in the fashion {|P1 -> 2 | P2 -> 5 | P3 -> 7 | P4 -> 11 | ... |},
Can I prove that 3Pn > Pn+1? My gut is kind of telling me it's true, but I'm not really sure how to go about proving (or disproving) it without knowing something…
Ozymandias
- 11
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calculating gravitational constant using Semi-major axis and orbit period
I have been having trouble calculating the gravitational constant (G) using Kepler's third law.
given Mercury has a semi-major axis of 0.39 AU, and an orbital period of 0.24 years, and that the sun has a mass of $1.989 * 10^{30} kg$, I tried to…
RIVERMAN2010
- 101
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Please explain this move in a simple polynomial proof
Trying to find when: $x^3+2x^2y+2xy^2+y^3=0$
The solution in my book makes the observation: $(x+y)^3=x^3+3x^2y+3xy^2+y^3$
This is similar to our equation with the difference being: $x^2y+xy^2$
Simplify to: $xy(x+y)$, and we see that this is equal to…
lopan
- 55
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A notion of relabelling sets
I read an article and find a statement in the proof that I highlighted below.
I do not understand, why we can do relabelling?
And I do not know, how to do relabelling based on statement above?
Can I relabel, for example, $I_{1,0}=X_2$,…
user136524
- 415
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1 answer
Why is the value of the coefficient $a_0=-1/2$ in this product of two series?
I've read this answer here and know why $a_{-1}=1$ but I really don't get how $a_0=-\frac{1}{2}$.
Here is the equation in question:
$$\left(\sum_{n\ge0}a_{n-1}z^n\right)\left(\sum_{n\ge0}\frac{z^n}{(n+1)!}\right)=1.$$
I can only see that…
Quotenbanane
- 1,594
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0 answers
Difficult theorem to prove.
My professor said that $P=NP$. I believe him, but am struggling to prove this to be true. I have been staring at this equation for hours, and at this point am completely befuddled. Someone please help.
My professor also said anyone who proves it…
Ethan
- 9
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Proof explanation - Erdös-Szekeres (1960)
At this paper, on Section 2, it is constructed a set of $2^{n-2}$ points in the plane such that they do not contain a convex $n$-gon.
I am not able to grasp it. I get lost when it says:
Suppose now that $P_i, (i = 1, \dots,r)$ is a non-empty subset…
Juan Moreno
- 1,110
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1 answer
Omission of the convexity hypothesis in the case of the projection theorem in a Hilbert space.
I did not understand the following example concerning the omission of the convexity hypothesis in the case of the projection theorem in a Hilbert space.
let $Q$ the set of sequence $$x^{(n)}=\left(x_k^{(n)}\right)\in l^2$$ defined as…
NatMath
- 910
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1 answer
proof with prime numbers that is reflexive, symmetric and transitive
I have found the following problem and try to solve it by myself, but I have some doubts about it. The problem is the following:
A binary relation P is defined on Z as follows: For all $m,n\in \mathbb{Z},mPn\Leftrightarrow \exists$ a prime number p…
Lila
- 479