How is Inaccessible Cardinal Written?

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Discussion Overview

The discussion centers around the notation or symbol used to represent inaccessible cardinals in set theory, including concepts like Aleph Null and the Absolute Infinite. Participants explore various symbols and their meanings, as well as the philosophical implications of these concepts.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant inquires about the notation or symbol for inaccessible cardinals, mentioning that symbols resembling Theta and phi have been used.
  • Another participant provides a link to a Wikipedia article on inaccessible cardinals, suggesting it may contain helpful information.
  • A participant notes that the Wikipedia article does not provide a symbolic representation and references another article discussing the Absolute Infinite, questioning its relation to inaccessible cardinals.
  • Concerns are raised about the concept of Absolute Infinite, with one participant expressing confusion about its implications, such as what it means to multiply it by 2.
  • Another participant comments on the philosophical nature of the Absolute Infinite, suggesting that if it were not considered weird, it would not be inconceivable, referencing a philosophical term related to such concepts.

Areas of Agreement / Disagreement

Participants express uncertainty about the notation for inaccessible cardinals and engage in a debate regarding the concept of Absolute Infinite, with no consensus reached on its meaning or implications.

Contextual Notes

There are limitations in the discussion regarding the definitions and interpretations of symbols and concepts, as well as the philosophical aspects that remain unresolved.

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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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?
 
I have no expertise in this area. However, the concept of Absolute infinite sounds weird to me. What is Absolute infinity times 2? etc.
 
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.
 

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