Bitcoin Forum

What are the simplest axioms we can use to describe 0 and 1 (before well-ordering etc....)?

I don't think this will get many replies.

ugh.... I thought the bitcoin community was filled with Mathematic fans.....

:/

No Mathematics fans here only miners.

I wouldn't say so. If you look hard enough - eventually you will find someone who is into math :D

You've got to be in it to win it.

Jesus Christ.

no one likes math except for math teachers

I like Math. I just don't love it.

Indeed, Math is okay, but it's not like I think about it when I'm horny.

ego and soul

dankkkk?

How's your 30+ loss streaks treatin ya?

?

do you use the username "dankkk" when you're in JD or PD chat?

in the real number corpse

the neutral is the real number with property

1.X=X.1=X  where X is any real number and "." is the mulktipplication as defined in R

the zero is the real number with the property

0.X=X.0=0  where X is any real number and "." is the multiplication as defined in R

they are unique by definition (easy to prove)


Not sure it's a mathematical answer you wanted tought

eh kinda. That was something similar my professor showed me but with Natural numbers since using real numbers is not allowed until you define them which requires much more proof.


I was kinda just going for the number 0.

0 has certain properties which we can accept as axioms.
1 has certain properties which we can accept as axioms.


0 = empty set
1 = {empty set}
2 = [empty set, 1}

etc...

well if you want to go with the naturals, of course everything is axiomatic: it 's a group whith the property "if it contains a natural number then it contains the next one"

if X belongs to N (natural numbers group) then X+1 belongs to N

1 and 0 being defined as in my previous post:

N={0,1,1+1=2,2+1=3,........}

the thing is the digits from 0 to 9 are just made up as they were needed at a time. so the building properties of the group is axiomatic and if you want to deny it, well you have to make up your own maths there

Maths is bore ! i didn't like to study math how can tell answer of this question very difficult to me

so what axioms do we use to define natural numbers?

What is the simplest one?

yeah it's a first year of math superior studies i think. but it's not that complicated honestly. basically what he is asking is "how did we build the mathematical objects 1 and 0"
and the answer is easy:

because we needed them, digits are the building blocks of numbers then group of numbers build up into other groups and so on. If you want a full proof of real numbers and it's 10 properties then just check basics of linear algebra.

axiom to define natural number group is: 1)it contains 0
                                                 2)if it contains any x then it contains this x +1
so if it contains 0 then it contains 1
if it contains 1 then it contains 2
and so on...

what do we define X to be?

x being a natural ofc

lol I'm pretty sure you can't define x to be a natural number if we're trying to build them from scratch.

No

ah okay. Never mind then that comment wasn't directed towards you.

you can because (1) defines N as a non-empty group