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
3
votes
2 answers
Why is $0^0$ undefined and how would we graph this?
So I saw exponents like $3^0$ and $4^0$, etc which are all equal to $1$.
And then soon I see that $0^0$ is not defined.
I checked the graph of $x^0$
Then I decided to make some observations.
We go like this:
$0.9^{0.9} = 0.909532576$
$0.8^{0.8} =…
user880107
3
votes
2 answers
Two norms on a linear vector space are equivalent if and only if every set that is bounded in one of the norms is bounded in the other norm.
I want to prove the following statement:
Two norms $\| \cdot \|_1$ and $\| \cdot \|_2$ on a linear vector space $X$ are equivalent if and only if every set that is bounded in one of the norms is bounded in the other norm.
(Note that going from…
tobias
- 55
3
votes
2 answers
Simplifying $ \tan 2x = 5 \cos 2x$
My son asked for help with his maths homework last night. The question was to show that $$\tan (2x) = 5\sin(2x)$$ can be written as $$\sin(2x)(1-5\cos(2x))=0$$ My first response was to rearrange as $\tan (2x) - 5\sin(2x) = 0$, replace $\tan$ with…
Kevin O'Donovan
- 133
3
votes
3 answers
Making a distinction between "fact" and "assumption"
Consider following proof:
Prove that if $x^2 + y = 13$ and $y ≠ 4$ then $x ≠ 3$.
Proof. Suppose $x^2 + y =
13$ and $y ≠ 4$. Suppose $x = 3$. Substituting this into the equation
$x^2 + y = 13$, we get $9 + y = 13$, so $y = 4$. But this…
Stokolos Ilya
- 3,371
3
votes
1 answer
Confusing step in the proof of convergence of Expected Sarsa
The proof of convergence of Expected Sarsa is presented in A Theoretical & Empirical Analysis of Expected Sarsa. This proof is similar to the proof of convergence of Sarsa, presented in Convergence Results for Single-Step On-Policy…
renatoc
- 141
3
votes
2 answers
What is the last nonzero digit at the end of 10!?
What is the last nonzero digit at the end of $10!$ ? What is the last nonzero digit at the end
of $100!$ ? What is the last nonzero digit at the end of $1,000,000!$?
Is there a formula to find out the pattern?
anonymous9254
- 97
- 1
- 3
3
votes
1 answer
Velleman: Section 3.3 Ex 15 p.122 Intersections of indexed families of sets
I've been learning a lot from this book, but have found myself entirely stuck with this seemingly trivial question. I think it's due to a lack of understanding of how to treat universal quantifiers with indexed families of sets.
The question…
abvariant
- 33
3
votes
6 answers
What does $\epsilon > 0$ is arbitrary mean?
I was browsing a proof here. At the end of the proof, the author says:
$\operatorname{diam}(\bar{E}) \leq \operatorname{diam}(E)+ε.$ Since $\epsilon > 0$ is arbitrary, $\operatorname{diam}(\bar{E}) \leq \operatorname{diam}(E)$.
I'm not sure how…
user1691278
- 1,361
3
votes
1 answer
Strategy of Helfgott when proving Weak Goldbach Conjecture
In 2013, Harald Helfgott proved that the weak Goldbach conjecture (now a theorem) which states that every odd number grater than $5$ is sum of three primes.
My question: What was his strategy when he is proving the statement above?
user429582
3
votes
2 answers
Proving Pascal 's identity, still a struggle
${n-1 \choose k-1} + {n-1 \choose k} = {n \choose k}$
My start:
$$\begin{align}{n-1 \choose k-1} + {n-1 \choose k} &= \frac{(n-1)!}{(k-1)!(n-k)!} + \frac{(n-1)!}{(k!)(n-k-1)!}\\
&= (n-1)! \times \Big(\frac{1}{(k-1)!(n-k)!} +…
K. Gibson
- 2,381
3
votes
3 answers
What is the difference between a formula and a proof?
As I understand it, a formula is a method for solving a mathematical problem expressed using alpha numeric characters like the quadratic formula is a method for solving quadratic equations when factoring will not work. I understand a proof to be a…
Mr. Concolato
- 163
3
votes
0 answers
Explanation of a Proof for the Chevalley-Warning Theorem
I can see how the power sum is applicable in the final paragraph of the proof, but it's still too vague in my head. Can anyone provide more details as to why the power sum of each monomial vanishes? The lemma in reference can be found here. When we…
user240033
- 161
2
votes
1 answer
What's the name of this formula? Proof solution.
I am working through the problems from the Book of Proofs. I am feeling rather dejected since after spending close to 3 hours looking at the problem unable to unlock the last step, the proof involved a formula I had never heard off.
I am wondering…
Solar
- 99
2
votes
4 answers
How did people come up with the formula $a^3+b^3=(a+b)(a^2-ab+b^2)$?
Every resource that I've read proves the formula
$$ a^3 + b^3 = (a+b)(a^2-ab+b^2) \tag1$$
by just multiplying $(a+b)$ and $(a^2 - ab + b^2)$.
But how did people come up with that formula? Did they think like, "Oh, let's just multiply these…
Rodion Iskhakov
- 113
2
votes
1 answer
Euclidean division algorithm, uniqueness: Why does it follow that r-r'=0?
As you know, it's about (informally) proving that for d and n there are q and r that are unique. We start with n = qd+r.
Remainder is smaller than d. 0 ≤ r < d.
Then we suppose that there are q' and r' so that qd+r = q'd+r'.
So far so good. But…
