How is Inaccessible Cardinal Written?

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In summary, the conversation discusses the notation and symbols used to represent inaccessible, strong, and uncountable cardinals in set theory. The Wikipedia article on inaccessible cardinals does not provide any symbolic representation, but the concept of Absolute Infinite (represented by the symbol Ω) is an extension of the idea of infinity proposed by mathematician Georg Cantor. However, the concept of Absolute Infinite may be considered strange as it is inconceivable and cannot be multiplied by a finite or transfinite quantity.
  • #1
shintashi
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I'm writing some notes on set theory, Aleph Null, etc., and was wondering if there's a Notation or Symbol that abbreviates this (inaccessible/strong/uncountable etc. cardinals). I'm not sure if I've seen notation before but it seems like symbols resembling Theta and phi have been used.
 
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  • #3
I have been to that wiki article and could not find where it labeled itself symbolically.

Did find this: under this other wiki article: https://en.wikipedia.org/wiki/Absolute_Infinite
"The Absolute Infinite (symbol: Ω) is an extension of the idea of infinity proposed by mathematician Georg Cantor.

It can be thought as a number which is bigger than any conceivable or inconceivable quantity, either finite or transfinite.
"
However I don't think Cantor or infinite series mathematicians believe the omega from absolute infinite is the same as an uncountable/strong inaccessible cardinal.
Correct me if I am mistaken?
 
  • #4
I have no expertise in this area. However, the concept of Absolute infinite sounds weird to me. What is Absolute infinity times 2? etc.
 
  • #5
if it didn't sound weird, how could it possibly be inconceivable? There's a philosophy term for this stuff "Noumenal" stuff we aren't supposed to make sense of.
 

1. How is the term "Inaccessible Cardinal" defined?

The term "Inaccessible Cardinal" refers to a type of cardinal number in set theory that is greater than all smaller cardinal numbers, but cannot be reached by the process of taking the power set or union of smaller cardinal numbers.

2. What is the notation used to represent Inaccessible Cardinal?

Inaccessible Cardinal is typically denoted by the letter "κ" in set theory notation.

3. How is Inaccessible Cardinal related to the concept of infinity?

Inaccessible Cardinal is a type of infinity, specifically an uncountable infinity. It represents the size of a set that cannot be reached by any finite process of counting or construction.

4. How are Inaccessible Cardinal numbers used in mathematics?

Inaccessible Cardinal numbers are primarily used in set theory and mathematical logic to study the properties of infinite sets and their cardinality. They also have applications in other branches of mathematics, such as topology and analysis.

5. Can Inaccessible Cardinal numbers be proven to exist?

The existence of Inaccessible Cardinal numbers is a controversial topic in mathematics. While it is not possible to prove their existence within the standard axioms of set theory, many mathematicians accept their existence based on various mathematical constructions and arguments.

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