Can we define a well ordered set just like a totally ordered set having the least element?
Namely, is the statement "the toset T has the least element" equivalent to "any non empty subset of the toset T has the least element"?
Regards.
2026-03-27 10:44:48.1774608288
Alternative definition o a well order
40 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ORDER-THEORY
- Some doubt about minimal antichain cover of poset.
- Partially ordered sets that has maximal element but no last element
- Ordered set and minimal element
- Order relation proof ...
- Lexicographical covering of boolean poset
- Every linearly-ordered real-parametrized family of asymptotic classes is nowhere dense?
- Is there a name for this property on a binary relation?
- Is the forgetful functor from $\mathbf{Poset}$ to $\mathbf{Set}$ represented by the object 2?
- Comparing orders induced by euclidean function and divisibility in euclidean domain
- Embedding from Rational Numbers to Ordered Field is Order Preserving
Related Questions in WELL-ORDERS
- Proof of well-ordering property
- how to prove the well-ordering principle using the principle of complete mathematical induction
- Role of Well-Ordering Principle in proving every subgroup of $\mathbb{Z}$ is of the form $n\mathbb{Z}$
- Is Induction applicable only to well-ordered sets that are not bounded above?
- Application of the Well-Ordering Principle
- Equinumerous well ordered sets are isomorphic
- How can a set be uncountable but well-ordered?
- well ordering principle and ordered field
- Can you turn a well-founded relation into a well-quasi-ordering?
- Initial segment of $\mathbb{Z}$ not determined by an element
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?
No, those are not equivalent.
The non-negative reals $[0,\infty)$ with the usual ordering have a least element (namely $0$) but are not well-ordered because the subset $(1,2)$ does not contain a least element.