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
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. 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
0:00 js woke up. same breakfast every day. coffee, persimmon, muesli, yogurt pic.twitter.com/5XUhCLi2kz
posted at 00:23:46