I was going about this by trying to come up with a bijection between this set and the set of all infinite sequences of zeros and ones (like 010100....), which I know in uncountable. But I didn't have much success. Other thoughts on how to get started?
2026-03-29 16:21:03.1774801263
Prove that the set of complete & transitive relations on a countably infinite set is uncountable
162 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in REAL-ANALYSIS
- how is my proof on equinumerous sets
- Finding radius of convergence $\sum _{n=0}^{}(2+(-1)^n)^nz^n$
- Optimization - If the sum of objective functions are similar, will sum of argmax's be similar
- On sufficient condition for pre-compactness "in measure"(i.e. in Young measure space)
- 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
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Is this relating to continuous functions conjecture correct?
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Absolutely continuous functions are dense in $L^1$
- A particular exercise on convergence of recursive sequence
Related Questions in RELATIONS
- How are these definitions of continuous relations equivalent?
- Is a relation on which every element is related with itself alone transitive?
- Relation power composition
- Order relation proof
- Order relation proof ...
- How to identify if a given Hasse diagram is a lattice
- Is the relation < a strict total order?
- Is there a name for this property on a binary relation?
- Finding all reflexive binary relations of a set
- Showing that a relation is reflexive, symmetric and transitive
Related Questions in INFINITY
- Does Planck length contradict math?
- No two sided limit exists
- Are these formulations correct?
- Are these numbers different from each other?
- What is wrong in my analysis?
- Where does $x$ belong to?
- Divide by zero on Android
- Why is the set of all infinite binary sequences uncountable but the set of all natural numbers are countable?
- Is a set infinite if there exists a bijection between the topological space X and the set?
- Infinitesimal Values
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?
It is enough to come up with an injection from the set of infinite sequences of zeros and ones into the set of complete and transitive relations.
So suppose you have a sequence like $(a_n)=(0,1,0,1,0,0,\ldots)$. You want to define a relation $R$ that depends somehow on $(a_n)$. You're going to say that $iRj$ if and only if... [something to do with $a_i$ and $a_j$]. Can you come up with a definition that makes $R$ complete and transitive? And is the mapping from sequences to relations injective?