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 that k has at least two distinct factors other than 1 and k
$k = n^3 + 1$ and $n>2$
$n^3 + 1 = (n + 1)(n^2 - n + 1)$
Prove that $k$ has at least two factors other than itself and $1$.
Can someone help me with this proof but not with induction.
Joe
- 1
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2 answers
Prove function is a homomorphism
I'm having trouble trying to prove the following:
Let $G$ and $H$ be two groups and let $f:G\to H$, $g:H\to G$. Show that if $g$ is injective and $g$ and $g\circ f$ are homomorphisms, then $f$ too, is a homomorphism.
This is what I've done so…
downmath
- 329
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3 answers
Arranging $9$ numbers around a circle
I am trying to solve the below problem.
Suppose that five $1$s and four $0$s are arranged around a circle. Form a new circle by placing a $0$ between any two unequal adjacent numbers and a $1$ between any two equal values before then erasing the…
JohnT
- 1,368
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What does it mean that the functions are different only by the values they don't take.
Please explain how they are different, I am not able to follow this(see bold text below)
Definition. The identity function on the set $X$ is the function
$$
i d_{X}: X \longrightarrow X, \quad x \longmapsto x,
$$
which we also write as $i…
ALEXANDER
- 2,099
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1 answer
Proof problem about inequality
Question: Given x > sinx for x > 0, prove
πx - 2x^2 > sin2x for 0 < x < π/2
This is a problem about inequality that involves trig, I tried to divide the RHSs and LHSs by x > sinx to get π /2 - x > cosx, and stuck on it.
I am not sure the way I am…
Winnie Chan
- 11
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1 answer
I don't understand this step in the proof for the probability of coprimality
On wikipedia for the probability that two random numbers are coprime they give the following line $\left(\prod\frac{1}{1-p^{-2}}\right)^{-1}=\frac{1}{\zeta(2)}$ where $1-\frac{1}{p^2}$ is the probability that at least one of the two numbers are not…
Pen and Paper
- 1,371
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1 answer
A particular functional $\varphi$ such that $\varphi(\cdot)=0$
Let $V$ be a $\mathbb{K}-$vector space finite dimensional ($\mathbb{K}$ is a field). Let $v\in V$ be a vector.
Is there a non-zero linear functional $\varphi\colon V\to\mathbb{K}$ such that $\varphi(v)=0$?
I would like to know if this is true and…
user805324
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1 answer
Question to the proof: $2^n+1$ is divisible by 3 for every odd number n
I've came across this post:
Prove that $2^n +1$ is divisible by $3$ for all positive integers $n$.
and the very last comment suggests to prove the above statement through
$2^=(3−1)^ =3+(−1)^$
I don't quite understand how one can conclude the last…
Greta
- 11
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Why is this true? For any power of 9, modulo 10 is either 9 or 1.
How can I prove in generality that for every power of 9, 9^k mod 10 will be either 9 or 1?
I know I can give a few cases like 9^2 = 81 mod 10 = 1 etc, but is there a more general way to prove?
yowhatsup123
- 181
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2 answers
Given the inequality $2x < x^2 < 3x, x \in \mathbb{Z}^+$, why is dividing away $x$ invalid?
Given some compound inequality like $2x < x^2 < 3x, x \in \mathbb{Z}^+$, what is the reason why the common factor $x$ cannot be divided out? I haven't taken a general algebra course yet, but my hunch would be that the integers not being closed under…
Reece McMillin
- 125
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1 answer
How do I derive the michaelis menten equation (part 1)?
My textbook in chemistry ("Biochemistry", Stryer et. al 9th ed p. 246) states that:
$$[ES]=\frac{[E][S]}{K_m}$$
where [ES] is the concentration of the enzyme-substrate-complex, [E] is the concentration of enzyme and [S] is the concentration of…
Magnus
- 703
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Are there two contradictions in this proof that $\sqrt{2}$ is irrational?
In section 6.1 of Richard Hammack's Book of Proof, they use the following proof (by contradiction) that $\sqrt{2}$ is irrational.
Suppose that $\sqrt{2}$ is rational, such that
$$
\exists a,b \in \mathbb{Z}, \sqrt{2} = \frac{a}{b} \tag{1}…
mhdadk
- 1,403
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1 answer
Formal, step-by-step proof for "If $m ∈ Z$ is even, then $m^2$ is even", with no large logical leaps?
tl;dr How would you write a blog post containing the proof for "if $m ∈ Z$ is even, then $m^2$ is even", such that it contained all definitions/theorems/proofs which it depends on, all the way back to the "base" definitions/theorems/proofs? If too…
Lance
- 3,698
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1 answer
Quick question for a statement I'm trying to prove with an odd order...
Statement: Let $G$ be a group and $H$ a subgroup with $[G:H]=8$. Assume $G/H$ is a quotient group. If $g\in G$ has odd order, then $g\in H$.
I don't quite understand this concept of $[G:H] = 8$ and how it connects to proving an element in $G$ has an…
user898710
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2 answers
Mirror symmetry about the line $y = 1/x$
This seems like a very simple computation, but I don't fully understand it.
Consider the line $y = 1/x$ in the first quadrant (i.e., when $x \geq 0$). We fix a point $x_0$ and consider the line tangent to $y = 1/x$ at the point $x_0$.…
user861776
- 1,062