In the Wikipedia page for the axiom of infinity it states that the natural numbers are a subset of the set that the axiom defines. Then gives a way of extracting the numbers from it. However I'm curious about these non numerical elements of the infinite set. What do they look like and why are they in the set?
2026-03-25 23:09:31.1774480171
What is in $\mathbb{I} - \mathbb{N}$
92 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
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 FOUNDATIONS
- Difference between provability and truth of Goodstein's theorem
- Can all unprovable statements in a given mathematical theory be determined with the addition of a finite number of new axioms?
- Map = Tuple? Advantages and disadvantages
- Why doesn't the independence of the continuum hypothesis immediately imply that ZFC is unsatisfactory?
- Formally what is an unlabeled graph? I have no problem defining labeled graphs with set theory, but can't do the same here.
- Defining first order logic quantifiers without sets
- How to generalize the mechanism of subtraction, from naturals to negatives?
- Mathematical ideas that took long to define rigorously
- What elementary theorems depend on the Axiom of Infinity?
- Proving in Quine's New Foundations
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?
The axiom specifies some things that must be in $\Bbb I$, but does not specify that anything in particular is not in $\Bbb I$. If you take any set $a$, it could be in $\Bbb I$. Then all the sets in an inductive chain starting with $a$ must be in $\Bbb I$.