Title: Number zero and Number one [Set Theory] Post by: emsjvh on April 03, 2014, 10:52:11 AM What are the simplest axioms we can use to describe 0 and 1 (before well-ordering etc....)?
Title: Re: Number zero and Number one [Set Theory] Post by: dx5 on April 03, 2014, 11:04:18 AM I don't think this will get many replies.
Title: Re: Number zero and Number one [Set Theory] Post by: emsjvh on April 03, 2014, 11:05:26 AM I don't think this will get many replies. ugh.... I thought the bitcoin community was filled with Mathematic fans..... :/ Title: Re: Number zero and Number one [Set Theory] Post by: Equate on April 03, 2014, 11:06:21 AM 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. Title: Re: Number zero and Number one [Set Theory] Post by: Rias on April 03, 2014, 11:18:07 AM 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. Title: Re: Number zero and Number one [Set Theory] Post by: railzand on April 03, 2014, 11:54:50 AM What are the simplest axioms we can use to describe 0 and 1 (before well-ordering etc....)? You've got to be in it to win it. Title: Re: Number zero and Number one [Set Theory] Post by: emsjvh on April 03, 2014, 07:37:50 PM What are the simplest axioms we can use to describe 0 and 1 (before well-ordering etc....)? You've got to be in it to win it. Jesus Christ. Title: Re: Number zero and Number one [Set Theory] Post by: Kiki112 on April 03, 2014, 08:21:49 PM 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. no one likes math except for math teachers Title: Re: Number zero and Number one [Set Theory] Post by: emsjvh on April 03, 2014, 08:32:15 PM 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. no one likes math except for math teachers I like Math. I just don't love it. Title: Re: Number zero and Number one [Set Theory] Post by: Acidyo on April 03, 2014, 08:48:21 PM 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. 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. Title: Re: Number zero and Number one [Set Theory] Post by: dank on April 03, 2014, 08:51:56 PM ego and soul
Title: Re: Number zero and Number one [Set Theory] Post by: emsjvh on April 03, 2014, 10:18:00 PM dankkkk?
How's your 30+ loss streaks treatin ya? Title: Re: Number zero and Number one [Set Theory] Post by: dank on April 04, 2014, 03:34:07 AM ?
Title: Re: Number zero and Number one [Set Theory] Post by: emsjvh on April 05, 2014, 03:31:30 PM do you use the username "dankkk" when you're in JD or PD chat?
Title: Re: Number zero and Number one [Set Theory] Post by: mighty jol on April 05, 2014, 03:43:58 PM 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 Title: Re: Number zero and Number one [Set Theory] Post by: emsjvh on April 05, 2014, 06:00:38 PM 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... Title: Re: Number zero and Number one [Set Theory] Post by: mighty jol on April 05, 2014, 06:23:25 PM 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 Title: Re: Number zero and Number one [Set Theory] Post by: bitkanu on April 05, 2014, 06:26:06 PM Maths is bore ! i didn't like to study math how can tell answer of this question very difficult to me
Title: Re: Number zero and Number one [Set Theory] Post by: emsjvh on April 05, 2014, 06:33:39 PM so what axioms do we use to define natural numbers?
What is the simplest one? Title: Re: Number zero and Number one [Set Theory] Post by: mighty jol on April 05, 2014, 06:37:13 PM 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... Title: Re: Number zero and Number one [Set Theory] Post by: emsjvh on April 05, 2014, 08:06:24 PM what do we define X to be?
Title: Re: Number zero and Number one [Set Theory] Post by: mighty jol on April 05, 2014, 08:08:37 PM x being a natural ofc
Title: Re: Number zero and Number one [Set Theory] Post by: emsjvh on April 05, 2014, 08:11:21 PM lol I'm pretty sure you can't define x to be a natural number if we're trying to build them from scratch.
Title: Re: Number zero and Number one [Set Theory] Post by: dank on April 05, 2014, 08:23:51 PM do you use the username "dankkk" when you're in JD or PD chat? No Title: Re: Number zero and Number one [Set Theory] Post by: emsjvh on April 06, 2014, 06:59:41 PM do you use the username "dankkk" when you're in JD or PD chat? No ah okay. Never mind then that comment wasn't directed towards you. Title: Re: Number zero and Number one [Set Theory] Post by: mighty jol on April 06, 2014, 07:07:34 PM you can because (1) defines N as a non-empty group
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