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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Difficult Q: Show that every integer $n$ can be written in the form $n = a^2 b$….product of distinct primes
I have a difficult two part question which has stumped me, the question is: Show that every positive integer $n$ can be written in the form $n = a^2 b$ for some integers $a$ and $b$ where $b$ is a (possibly empty) product of distinct primes, and how…
user431587
- 11
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How do I derive the quotient between these cumulant functions? A question concerning an argument in the book of Large Deviations from den Hollande
In the book of large deviations from den Hollander, in page 77 one reads
where $\rho_0 = \frac{1-\omega_0}{\omega_0}$ and equation VII.14 is
However, combining these two I have arrived at
$$\frac{\varphi(r,\omega)}{\tilde{\varphi}(r,\omega)} =…
Conrado Costa
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3 answers
Prove: $\exists M\in\mathbb{R}$ such that $\forall x\in (1,3)$, $\left|\frac{5x^2 - 2x - 4}{5(x^2 + 1)}\right|\leq M$
I am not sure how to find the correct upper and lower limits for this problem. I did find the breakdown of the inequality to be $\frac{5x^2+|2x|+4}{|5(x^2 + 1)|}$. Thanks for any help you can give!
Deryn21
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Using Peano Arithmetic, prove ss(0) + s(n) = sss(n).
I'm looking at a proof and failing to understand a step.
1) Base case:
$ss(0) + 0 = ss(0)$,
by the axiom for 0 addition which states that 0+n=n.
2) We want to prove that for all n,
$ss(0) + s(n) = sss(n)$.
By definition / axioms, we get the…
IgnorantCuriosity
- 1,423
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1 answer
Proof of Intermediate Value Theorem
If $f : [a, b] \rightarrow R$ is continuous
and $f(a) < 0 < f(b)$, then there is $a < c < b$ with $f(c) = 0$.
Proof.
We start to build a sequence of intervals $I_0 \supset I_1 \supset I_2 \supset \ldots$
such that $I_n = [a_n, b_n]$, and $f(a_n) < 0…
TripleA
- 1,503
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1 answer
Clarification of a proof as written in Margaris's book
In Angelo Margaris's book First Order Mathematical Logic it is written (see below),
Then,
Questions
In the above proof I don't understand what am I supposed to do at the second step. Can anyone explain that to me?
How from "$P$ admits $t$…
user170039
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1 answer
Proofs involving sets for $\{9^n: n∈ℚ\}=\{3^n: n∈ℚ\}$.
I need to prove that {9^n: n∈ℚ)={3^n: n∈ℚ).
So far I have proven {9^n: n∈ℚ}⊆{3^n: n∈ℚ}.
a∈{9^n: n∈ℚ}. Meaning for some a=9^n for some rational number. Thus, a=9^n=3^2n, showing that a is a rational number for some power of 3. so a∈{9^n:…
M.Maric
- 59
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Proving nth difference of squares
I'm a little stuck on proving $$(b^n-a^n)=(b-a)(a^0b^{n-1}+a^1b^{n-1}+ \cdots + a^{n-1}b^{0}).$$A solution I came across gave this as an answer:
$$(b-a)(b^n + b^{n-1} a+...+ba^{n-1} +a^{n} )\\
=(b-a)b^n + (b-a)b^{n-1} a+...+(b-a)ba^{n-1}…
Nikitau
- 1,353
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2 answers
What is wrong with this proof?2
(This is not homework)
Just to be sure, the reason why the proof is wrong because in line 2, they wrote x>= 0 and 1/x >=0 where we include zero. But, initial statement said to exclude zero. Also, 1/0 has no value/ meaning.
Math
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Understanding a projection function from S to B.
Let A and B be sets and $S \subseteq A \times B $ . Let $\pi_{1}$ be the projection function on $S$ to $A$ and $\pi_{2}$ be the projection function on $S$ to $B$. Give an example to show that.
$\pi_{2}$ need not be onto $B.$
Proof:
Let $A = \Bbb…
Jon
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Understanding how to approach a proof question that is related to using definitions.
I struggle doing these type of questions, i have no idea how i should approach these type of question. Like for example, the question below:
Suppose $f: A\to B$ is an injective function. Prove that $f^{-1}(f(C))=C $ for all $C \subseteq A$.
I now…
cosygod
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Simplifying the same function with different parameters
This is an extremely basic question but I am curious, can the same function be equivalent when it has different parameters.
For instance if let's say I had an equation p(r) = $ \frac {r}{a} $
I then had an equation
E = $ \frac{\int n(r')r}{n(r)}…
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1 answer
Proof of Cauchy Schwarz
In real analysis I we saw the following statement that was called the Cauchy - Schwarz inequality:
$|\vec{x}\cdot\vec{y}| \leq \lVert \vec{x} \rVert \lVert \vec{y} \rVert $.
This is the begin of the proof and there is a reasoning I don't…
user34
- 111
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Help with a biconditional divides proof
Prove the following
For any integer a, 14|a if and only if 2|a and 7|a.
I am stuck on how to prove this for the backwards implication case, that is if 2|a and 7|a then 14|a.
I get a=2k1 and a=7k2 for integers k1,k2,and a. Not sure where to go from…
Turing
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proof: For any real number $x$, if $x$ is not an integer, then $⌊x⌋+⌊-x⌋=-1$
My professor wrote this proof but i didn't understand some parts:
Suppose $x$ is a real number such that $x$ is not an integer. let $⌊x⌋=n$. By definition of floor and since $x$ is not an integer, $n
Omar
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