/sci/ - Science & Math » Thread #10892964

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Anonymous Fri 16 Aug 16:25:52 2019 No.10892964 View Reply Original Report

Quoted By: >>10892969 >>10894440

What's the cardinality of the number of digits of the decimal expansion of an irrational number? Do computable irrationals have a countably infinite number of digits and uncomputable irrationals an uncountably infinite number of digits?

Anonymous

Anonymous Fri 16 Aug 2019 16:28:58 No.10892969 Report

Quoted By: >>10892979 >>10893321

>>10892964
All numbers have an uncountably infinite number of digits in their decimal expansion. Even the integers. Just because they predictably repeat, it doesn't mean there aren't an uncountably large amount of them.

Anonymous

Anonymous Fri 16 Aug 2019 16:38:14 No.10892979 Report

Quoted By: >>10894440

>>10892969
Depends on your model of set theory. It's a theorem (shelah?) though that all reals have either aleph-2, aleph-4, or aleph-omega many digits

Anonymous

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Anonymous Fri 16 Aug 2019 19:32:43 No.10893303 Report

Quoted By: >>10894440

Rationals have alephnought digits Reals have 2^alephnought digits
Complexes have 2^alephone digits
Quaternions have 2^alephthree digits etc
You need that many digits to uniquely specify each type of number

Anonymous

Anonymous Fri 16 Aug 2019 19:38:59 No.10893321 Report

Quoted By: >>10894440

>>10892969
>Uncountably infinite number of digits in decimal expansion
>Irrational numbers written as decimals are just limits of an algebraic series
>A series indexed by N
>Uncountable
Kek

Anonymous

Anonymous Sat 17 Aug 2019 04:05:35 No.10894440 Report

Quoted By:

>>10892964

Clearly, the answers to these three questions as phrased are: $\aleph_{0}$ , yes, and no (check).

>>10892979
>>10893303

These posts contain erroneous claims (think).

>>10893321

This poster has the right idea.

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