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
0
votes
1 answer
If $x\neq 0$ then $\frac{1}{x}\neq 0$.
Field Axioms $M4$ and $M5$:
$M4$. There is a unique number $1$ such that $1 \ne 0$ and $(x)*(1)=x$ for all $x \in \mathbb{R}$
$M5$. For each $x \in \mathbb{R}$ with $x\ne 0$, there is a unique number $(\frac{1}{x})$ such that…
Skm
- 2,296
0
votes
2 answers
What is this set in this question? Measure theory proof
I have a question about the set $E_{kn}$, what is this? What are the parameters $n,k$ for? I guess actually $k$ is the real parameter because $n$ is fixed natural number. How are we cutting $f(x)$ here?
This was taken from Bartle
Lemon
- 12,664
0
votes
4 answers
Need help with direct proof
So I'm learning about direct proofs, and the first example shown is giving me a headache because I can't figure out how did the professor came up with the end solution. Here's what we need need to prove:
and the actual proof:
So, the third and the…
Zed
- 105
0
votes
1 answer
How can I prove a statement $A \vee B$, where $A$ and $B$ can't be proved by themselves?
Context: I'm working through Introduction to Algorithms (CLRS), in which one of the questions is:
Show that for any two functions $f(n)$ and $g(n)$ that are asymptotically nonnegative, either $f(n) = O(g(n))$ or $f(n) =…
Spongebob
- 25
0
votes
2 answers
Prove that the expression cannot be a power of 2
I have been boggled by this question for a while as well.
Prove that
$$(2a+b)(2b+a)=2^c$$
Is impossible.
I know that if a and b do exist then they must be even. I am trying to use this fact to contradict the statement. I haven also tried rewriting a…
user459239
0
votes
1 answer
Understanding G.H Hardy's Proof for Infinitely Many Rational Numbers
Taken from A Course of Pure Mathematics:
Irrational Numbers: If the reader will mark off on the line all the points corresponding to the rational numbers whose denominators are $1,2,3\ldots$ in succession, he will readily convince himself that he…
Crescendo
- 4,089
0
votes
2 answers
Proof that $2^{10}+5^{12}$ is a composite number
A hint or full answer will help a lot, because I have no idea what to do.
user410918
- 77
- 6
0
votes
2 answers
Proof by Cases not contradiction
"Show that if you pick three socks from a drawer containing just blue socks and black socks, you must get either a pair of blue socks or a pair of black socks."
I know how to solve this by contradiction but I am not sure how to solve it by Cases.…
Hidaw
- 971
0
votes
1 answer
Prove: there is a positive irrational number $x$ for which $x^2=3$.
I'm trying to prove
There is a positive irrational number $x$ for which $x^2=3$.
I think this would be useful.. but I'm not too sure. $\sqrt{2}\in\mathbb{R}\setminus\mathbb{Q}$
Ivy
- 225
0
votes
1 answer
Corollary of Lagrange's Theorem in Number Theory
Lagrange's Theorem: If $p$ is a prime and $$f(x)=a_nx^n+a_{n-1}^{n-1}+....+a_0, \text{ where }a_n\not\equiv 0\pmod p.$$ is a polynomial of degree $n\geq 1$ with integral coefficients, then the congruence $$f(x)\equiv 0\pmod p$$ has at most $n$…
Student
- 9,196
- 8
- 35
- 81
0
votes
1 answer
differential equation of exponential help understanting proof
If $\frac{d}{dx} e^x = e^x$ and $f:R\rightarrow R$ is a
differentiable function such that $f'(x)=af(x)$ with $a \in R$. Show
that there exist a real number $c$ such that $$f(x)=c*exp(ax)$$
Let $g(x)= f(x)exp(-ax)$…
Elina
- 227
- 2
- 9
0
votes
1 answer
Explanation for the proof of uniform convergence
I'm studying the uniform convergence and continuity and I could not understand the proof that is given in the book, could you explain the proof explicitly ?
Particularly,
Which method does it use in the proof ?
What is it's strategy ? etc.
Theorem:…
Our
- 7,285
0
votes
1 answer
How to prove that $f: \mathbb{N}^2 \to \mathbb{N}$ is a bijection?
I am being asked to prove that the following function $f: \mathbb{N}^2 \to \mathbb{N}$ is a bijection where:
$$f(x,y) = \frac{(x+y)(x+y+1)}{2} + y$$
So far I have not had any ideas on how to prove injection, and with regards to surjection I have…
GuPe
- 7,318
0
votes
1 answer
Why is this proof that a relation is transitive incorrect?
Suppose R is a relation on A, and S is a relation on P(A) (the power set of A) such that S = {(X,Y) ∈ P(A)×P(A)|(∃x∈X)(∃y∈Y)((x,y)∈R)}.
Thm: If R is transitive, then S is transitive.
Proof:
Assume R is transitive. Let (x,y)∈R and (y,z)∈R be…
IgnorantCuriosity
- 1,423
0
votes
1 answer
Prove a Property of Eulerian digraph
What is the proof of this property of an Eulerian digraph?
For every partition of the vertex set of an Eulerian digraph into two parts, A and B, the number of arcs from $A$ to $B$ denoted by $m(A,B)$ is equal to the number of arcs from $B$ to $A$…
Ong
- 233