Conjecture

[Anonymous No.14757584]

The number of occurrences of each digit from zero to nine within the first [math] n [/math] digits of [math] \sqrt{2} [/math] approaches to [math] \dfrac{n}{10} [/math] as [math] n [/math] approaches infinity.

Can you prove this?

[Anonymous No.14757601]

disproof: in base 4
>sqrt(2) = 1.122200213212121333032330302100202302332301031212322221111331..

[Anonymous No.14757630]

>>14757584
tautology

[Anonymous No.14757638]

>>14757601
Base 10 is special case. The generalized version of my conjecture is:

>The number of occurrences of each digit from zero to [math] b [/math] within the first [math] n [/math] digits on [math] \sqrt{2} [/math] in [math]\text{base-b}[/math] approaches to [math]\dfrac{n}{b}[/math] as [math] n [/math] approaches infinity.

[Anonymous No.14757657]

>>14757601
The generalized version of my conjecture is:

>The number of occurrences of each digit from zero to [math] b-1 [/math] within the first [math] n [/math] digits of [math] \sqrt{2} [/math] in [math]\text{base-b}[/math] approaches to [math]\dfrac{n}{b}[/math] as [math] n [/math] approaches infinity.

>>14757630
By occurrence I mean the occurrence of one individual digit.

[Anonymous No.14757688]

>>14757584
Proving that √2 is a normal number is extremely hard. Same for other irrational numbers such as π and e.

[Anonymous No.14758084]

I did a test on base-7 with seven million digits. So each digit should occur a million times. Here's the data on each digit.

0: 1 000 251
1: 999 671
2: 999 517
3: 1 000 633
4: 998 591
5: 1 001 898
6: 999 484

[Anonymous No.14758102]

>>14757584
>The number of occurrences of each digit from zero to nine
zero isn't a number. Neither is "root 2"(expression)

>>14757688
>Proving that √2 is a normal number is extremely hard.
It's proven not to be a number whatsoever.

[Anonymous No.14758219]

>>14757688
Does a proof even exist for any of them?

[Anonymous No.14758260]

>>14758219
Champernowne constant is both normal and irrational

[Anonymous No.14758282]

>>14758260
Obviuosly, I was asking about [math]\sqrt{2}[/math], [math]\pi[/math] and [math]e[/math]

[Anonymous No.14758347]

>>14757584
sqrt2 being normal is an open problem

[Anonymous No.14758352]

>>14758219
I believe it does not.

[Anonymous No.14758408]

>>14757584
Does this prove that triangles don't exist?

[Anonymous No.14758966]

>>14758102

[Anonymous No.14759171]

>>14757584
based if true
based if false

pretty interesting

I wouldn't assume homogenaity for a given precision. Ie perhaps the first 10000 digits is spread uniformly between 0-9 but not 150000