yuuki @yuuki26

i used the hashtag "want to connect with unschoolers".
#不登校さんと繋がりたい

no corresponding subtwt in english fsr.
#unschoolers #unschooling #homeschoolers #homeschooling #schoolrefusal #schoolavoidance #schoolanxiety

posted at 04:06:41

- hobbies: shogi/programming/math/english
- stan of: nothing
- fav game: pokemon go
- comments:
never drink or smoke / never get my driver's license / never fall in love or get married

posted at 03:31:24

- what's the acc for?: lifestreaming
- mainly tweet: my thoughts
- twitter stance: anything is OK
- what kind of ppl do u want to connect with?: ppl who share my hobbies
- free space:
5th grade~ unschooler / lives alone in late grandma's house / receives $700 a month from parents

posted at 03:31:23

my profile says 29age/male/NEET.

my pinned says:
lf friends

(2nd pic, made with https://prfmaker.com/m/479)
- name: yuuki
- tw id: @yuuki170
- account age: 2023~
- active hours: non-24-hour sleep-wake disorder https://twitter.com/yuuki170/status/1727315152121610747…

posted at 03:31:23

wanted an ai pfp but no different than me irl

cr: https://www.pixiv.net/artworks/110547305… https://pic.twitter.com/b4C6QKhLTu

posted at 01:18:18

started using my jpn acc.
i quote n translate some tweets on this acc smtm.
maybe once a month.
@yuuki170
https://x.com/i/user/1672629051419410435…

posted at 00:32:52

2023年11月21日(火)6 tweetssource

i decided to put my blog's source on Gist.
still under maintenance.
https://gist.github.com/yuuki15/6f4dd4a6ce7f5b23cd06f86394d17269…

posted at 23:13:30

I've uploaded some of my videos etc to http://archive.org.
hope they will remain until a future where youtube is gone.
https://archive.org/search?query=creator%3A%22yuuki+%E3%82%86%E3%81%86%E3%81%8D%28%E9%87%91%E9%87%8E%E8%A3%95%E5%B8%8C%29%22…

posted at 16:27:36

¹ this indicates "direct implications or relative consistency implications", tho.
(e.g., huge < supercompact)

in order of both size and strength:
• inaccessible < measurable < huge < rank-into-rank < 0=1

posted at 06:20:22

in the large picture,
• the size of a number
is proportional to
• how many numbers it can prove to be consistent.

the largest number proves the consistency of all numbers, including itself.
by Gödel's theorem, it is a "contradiction".

posted at 04:04:38

let us write Fin + Inf as ZFC.

similarly, if we add "a large cardinal exists", then we can prove the consistency of ZFC.
• ZFC + LC ⊢ Con(ZFC)

posted at 04:02:04

by Gödel's second incompleteness theorem, the axioms "finite numbers exist" can't prove their own consistency.
• Fin ⊬ Con(Fin)

now if we add "ℵ₀ exists", then we can prove the consistency of finite numbers.
• Fin + Inf ⊢ Con(Fin)

this shows Fin + Inf > Fin.

posted at 03:59:23

2023年11月20日(月)2 tweetssource

11月20日

so the Q is, what tf is the largest infinite number.
n it's a "contradiction" (aka 0=1).
as drawn in this pic.¹

let me explain from scratch. https://pic.twitter.com/YgwFaxEqFy

posted at 02:47:34

11月20日

actually, large cardinals refer to large with specific properties.

(the successor of an inaccessible cardinal is not inaccessible by definition.)

posted at 02:37:09

2023年11月18日(土)2 tweetssource

11月18日

¹ it is shown
• ℶ₁ ≠ ℵ₀ (Cantor)
• ℶ₁ ≠ ℵ_ω etc. (König's theorem)
tho.

posted at 21:58:42

11月18日

infinities are written
• ℵ₀, ℵ₁, ℵ₂, …, ℵ_ω, …
in order from smallest to largest.

for the number of reals ℶ₁,
• ℶ₁ = ℵ_?
is not provable from the standard axioms of mathematics.¹

the ℶ₁ = ℵ₁ conjecture is called the
• continuum hypothesis (CH).

posted at 21:50:24

2023年11月15日(水)1 tweetsource

11月15日

actually, there's infinitely many infinite numbers. https://pic.twitter.com/AnPs6LTbt4

posted at 11:12:06

2023年11月12日(日)8 tweetssource

¹ already known to the Jains of India (400 BC), tho.
but they made mistakes such as the number of points on a line |ℝ| and a plane |ℝ²| are not equal. (both are 2^ℵ₀.)

posted at 23:17:26

actually, the number of natural, integer, and rational numbers are all the same.

that infinite number is called ℵ₀ (aleph zero) or ℶ₀ (beth zero).

Cantor (1874) proved that the number of reals is larger than that.¹
that is called 𝔠 = 2^ℵ₀ = ℶ₁ (beth one).

posted at 23:15:52

the idea that having the same number is the same as having a 1-1 correspondence is called
• Hume's principle.¹

¹ neither Hume nor Galileo thought it applied to , tho (unlike Cantor).

posted at 21:40:16

have a look at this strange pic.
there's 2 circles.
a big one and a small one.

however, both circles consist of the same number of dots.
(there's a 1-1 correspondence.)
https://blog.wolframalpha.com/2010/09/10/transfinite-cardinal-arithmetic-with-wolframalpha/… https://pic.twitter.com/rFQ4ORGxea

posted at 21:32:01

is such a strange thing.
the whole and part can be the same size.¹
cf.
• Galileo's paradox.

¹ contrary to Euclid's 5th Common Notion (300 BC).
although some say that some CNs are by, e.g., Theon of Alexandria (4c).

posted at 21:16:42

mathematically, the answer is A
they're the same.
(even tho evens are part of integers.)

this is bc one integer corresponds to one even.
1 ↦ 2
2 ↦ 4
3 ↦ 6
4 ↦ 8
5 ↦ 10
︙
n ↦ 2n
︙

posted at 13:53:58

A) same bc they're infinite
B) infinity can't be compared
C) integers ofc bc evens are only half of them

posted at 09:44:10

let me explain from scratch.

Q: which is greater,
• the number of all integers
• the number of all even numbers

both are infinite.
there's many ways to think abt it.

posted at 09:42:34

2023年11月11日(土)3 tweetssource

11月11日

mathematicians consider infinity a number.

this is bc in the 19c, a man named Cantor found that there are "multiple infinities".
i.e., infinity 1, infinity 2, infinity 3, ….

just like 1, 2, 3, ….
can also do arithmetic with .

posted at 08:13:31

11月11日

im summarizing my tweets here rn
https://min.togetter.com/kb628xT

posted at 07:48:57

11月11日

The largest number is a "contradiction".
let me explain this.

u may be reminded of a googolplex or graham's number.
the problem is: graham's number+1 is larger.

they're still finite.

posted at 07:38:31

2023年11月10日(金)1 tweetsource

11月10日

i forgot dominoes

posted at 14:30:00

2023年11月08日(水)12 tweetssource

what's tricky is numbers go on forever.
1, 2, 3, 4, … is only the beginning.
large numbers beyond graham's number are still "natural numbers".

(ultrafinitists deny the existence of numbers that are too large.)

posted at 12:55:47

note commutativity, distributivity etc can be proved by a method called induction (other than using lego).

posted at 10:35:16

philosophically, there can be 2 ways of thinking:
• numbers are such code in reality
• no, such code are just a miniature model of numbers

i stand with the former,
but on 2nd thought the latter may be more rational.

posted at 10:14:40

sounds like there's a kinda programming language within math.
numbers can be programmed/coded with it.

there could also be implementations on a computer, such as Lean.

posted at 08:52:51

just as atoms are made of elementary particles, it seems that numbers can be made from sets, functions (church encoding), or categories (or topoi).

as sets:
0 = {}
1 = {{}}
2 = {{}, {{}}}
3 = {{}, {{}}, {{}, {{}}}}

posted at 07:33:27

there's a definition of numbers called
• Peano axioms.
i haven't figured it out yet.

posted at 06:20:21

when we ask smtg like "why does 1+1=2?", it is said that we face the so-called
• Münchhausen trilemma.

posted at 05:54:03

marbles, number lines, or areas of figures can be used as well.
i suspect one aspect of these is the "unary numeral system".

like
3 + 4
= 111 + 1111
= 1111111
= 7.

posted at 05:21:44

cr: https://www.resolve.edu.au/algebra-odds-and-evens… https://commons.wikimedia.org/wiki/File:Square_number_16_as_sum_of_gnomons.svg…

posted at 04:47:19

Lego bricks can be used for visualizing numbers.

parity arithmetic:
even + even = even
even + odd = odd
odd + odd = even

sum of odd numbers:
1 + 3 + 5 + … + (2n - 1) = n²

it has limitations and it's hard to believe that lego is the nature of numbers. https://pic.twitter.com/KLgXwtTZDC

posted at 04:47:18

• What are numbers?
i mean,
• What is the nature of natural numbers?

Conclusion: it's hard.

it's a fundamental question, but not an easy one to answer.
it's better to pretend to know such "obvious" things and move on.

posted at 02:59:28