Cryptocurrency Q&A
How big is aleph-1?
How big is aleph-1?
HanbokGlamourQueenEleganceBloom
Thu Oct 24 2024
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7
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I'm curious about the size of aleph-1. I've heard it's a concept related to infinity, but I'm not sure exactly how to quantify its magnitude. Could someone explain how big aleph-1 is?
7 answers
CryptoEagle
Sat Oct 26 2024
This peculiar characteristic of ℵ1 underscores its significance in the study of infinite sets.
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Elena
Sat Oct 26 2024
When the axiom of choice is introduced into the equation, the landscape of cardinal numbers changes slightly.
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CryptoGuru
Sat Oct 26 2024
The concept of ℵ1, or aleph-one, holds a unique position in the realm of mathematics.
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Emanuele
Sat Oct 26 2024
With the axiom of choice, it becomes possible to prove that the class of cardinal numbers forms a totally ordered set.
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DondaejiDelight
Sat Oct 26 2024
Specifically, within the framework of ZF set theory, which stands for Zermelo–Fraenkel set theory without the axiom of choice, ℵ1 signifies a cardinal number that lacks any intermediary between ℵ0, the countably infinite cardinal, and itself.
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