Let M be the monoid of rational functions under composition. What are the possible orders of elements of M? $1$ is possible using the function $x$. $2$ is possible using the function $-x$. $3$ is possible using $\frac{-1}{1+x}$. $\infty$ is possible using the function $1+x$. Are there any other possible orders of elements?
2026-03-29 16:02:49.1774800169
What are the possible orders of rational functions under composition (with coefficients in the reals)?
22 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 RATIONAL-FUNCTIONS
- Find $\lim_{(x,y)\to(0,0)}\frac{x^3y^2}{x^4+y^4}$
- Advice on simple exercise; dividing rational expression
- Is this symmetric rational function known?
- Points of discontinuity of Rational Functions
- Degree of a Rational Mapping
- Using Eisenstein's Criterion on something besides an integer
- Finding the equation of a rational function from a set of constraints
- How does the convergence sector of a continued fraction depend on the order where it is truncated?
- Rational functions examples
- A rational function with hidden symmetry and alternating poles and zeros.
Related Questions in MONOID
- What concept does a natural transformation between two functors between two monoids viewed as categories correspond to?
- Monoid but not a group
- In a finite monoid (M, $\circ$) if the identity element $e$ is the only idempotent element, prove that each element of the monoid is invertible.
- Maps between free commutative monoid monad and the free monoid monad
- Do Monoid Homomorphisms preserve the identity?
- Finitely Generated Free Group to Finitely Generated Free Monoid
- free commutative monoid monad
- Let $M$ be a monoid and let $M^*$ be the group of invertible elements of $M$. Prove the following...
- Monoid ring over a field is a finitely generated $k$-algebra
- a generalization of group (monoid with order-by-order invertible elements)
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?