Define an equivalence relation on the set R that partitions the real line into subsets of length 1.
2026-03-28 10:02:14.1774692134
Equivalence relation and partitions
868 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ABSTRACT-ALGEBRA
- Feel lost in the scheme of the reducibility of polynomials over $\Bbb Z$ or $\Bbb Q$
- Integral Domain and Degree of Polynomials in $R[X]$
- Fixed points of automorphisms of $\mathbb{Q}(\zeta)$
- Group with order $pq$ has subgroups of order $p$ and $q$
- A commutative ring is prime if and only if it is a domain.
- Conjugacy class formula
- Find gcd and invertible elements of a ring.
- Extending a linear action to monomials of higher degree
- polynomial remainder theorem proof, is it legit?
- $(2,1+\sqrt{-5}) \not \cong \mathbb{Z}[\sqrt{-5}]$ as $\mathbb{Z}[\sqrt{-5}]$-module
Related Questions in ELEMENTARY-SET-THEORY
- how is my proof on equinumerous sets
- Composition of functions - properties
- Existence of a denumerble partition.
- Why is surjectivity defined using $\exists$ rather than $\exists !$
- Show that $\omega^2+1$ is a prime number.
- A Convention of Set Builder Notation
- I cannot understand that $\mathfrak{O} := \{\{\}, \{1\}, \{1, 2\}, \{3\}, \{1, 3\}, \{1, 2, 3\}\}$ is a topology on the set $\{1, 2, 3\}$.
- Problem with Cartesian product and dimension for beginners
- Proof that a pair is injective and surjective
- Value of infinite product
Related Questions in EQUIVALENCE-RELATIONS
- Relations of equivalence...
- Number of subsets, relations etc of a set
- Number of possible equivalence relations
- Why is $p(z) = \frac{e^z}{1 + e^z} \color{red}{\equiv} \frac{1}{1 + e^{-z}}$ and not $=$?
- Simple question about relations
- Total number of equivalence class for a set
- Is this an equivalence relation and explaination?
- Partition of a set identified by a equivalence relation
- Define an equivalence relation on $\{ 1,2,3,4 \}^2$ by: (, )(, ) if ⋅ = ⋅ . How many equivalence classes are there?
- Prove that $\sum_{i=1}^n\lvert[a_i]\rvert$ is even iff $n$ is even
Related Questions in SET-PARTITION
- Existence of a denumerble partition.
- Given N sets of partitions, find a partition such that it satisfies a criterion
- Given a decreasing family of sets and partitions with a refinement condition, is there a monotonous choice function from the partitions?
- Partition of an $n$-element set such that the smallest component has at least $k$ elements?
- Number of equivalence relations on a set with $kn$ elements with the condition that each equivalence class has n elements
- Is there a similar notion of cycle type commonly in use for finite partitions, where instead of cycle sizes one counts the block sizes?
- Is it possible to construct two subsequences of a sequence X with specific properties such that the two subsequence sums are the same?
- Coloring $\mathbb{R}^2$ and single-colored paths
- A homework problem about set theory
- Canonical name for the partition that a partition of a set induces on its subsets
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's actually easiest to work backwards on this problem. We first define the ste of equivalence classes, $$\{[n,n+1):n \in \mathbb{Z}\}$$ and say $x,y \in \mathbb{R}$ are equivalent if they belong to the same equivalence class.
Any set partition gives rise to an equivalence relation in this way.
(This is the same as Stefan H.'s comment, but there's not much else you can do, other than shift the segments. Or perhaps you could break them into disjoint segments with total length $1$.)