Let $f,g$ be positive functions. Prove or disprove: $$ \frac{O(f(n))}{O(g(n))}=\frac{\Omega(f(n))}{\Omega(g(n))} $$ I can't seem to figure out this statement. I could not think of an example that disproves it. I also could not find a way to prove it. How should I solve it?
2026-04-02 21:40:36.1775166036
Proving or disproving: $\frac{O(f(n))}{O(g(n))}=\frac{\Omega(f(n))}{\Omega(g(n))}$
52 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ASYMPTOTICS
- Justify an approximation of $\sum_{n=1}^\infty G_n/\binom{\frac{n}{2}+\frac{1}{2}}{\frac{n}{2}}$, where $G_n$ denotes the Gregory coefficients
- How to find the asymptotic behaviour of $(y'')^2=y'+y$ as $x$ tends to $\infty$?
- Correct way to prove Big O statement
- Proving big theta notation?
- Asymptotics for partial sum of product of binomial coefficients
- Little oh notation
- Recurrence Relation for Towers of Hanoi
- proving sigma = BigTheta (BigΘ)
- What's wrong with the boundary condition of this $1$st order ODE?
- Every linearly-ordered real-parametrized family of asymptotic classes is nowhere dense?
Related Questions in COMPUTER-SCIENCE
- What is (mathematically) minimal computer architecture to run any software
- Simultaneously multiple copies of each of a set of substrings of a string.
- Ackermann Function for $(2,n)$
- Algorithm for diophantine equation
- transforming sigma notation into harmonic series. CLRS A.1-2
- Show that if f(n) is O(g(n) and d(n) is O(h(n)), then f(n) + d(n) is O(g(n) + h(n))
- Show that $2^{n+1}$ is $O(2^n)$
- If true, prove (01+0)*0 = 0(10+0)*, else provide a counter example.
- Minimum number of edges that have to be removed in a graph to make it acyclic
- Mathematics for Computer Science, Problem 2.6. WOP
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Big O's on the LHS can be arbitrarily small. Big Omega's on the RHS can be arbitrarily big. It is easy to construct counterexamples following this logic.