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Topic: Number zero and Number one [Set Theory] (Read 741 times)

member
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April 06, 2014, 03:07:34 PM
#26
you can because (1) defines N as a non-empty group
full member
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April 06, 2014, 02:59:41 PM
#25
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.
legendary
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You cannot kill love
April 05, 2014, 04:23:51 PM
#24
do you use the username "dankkk" when you're in JD or PD chat?



No
full member
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April 05, 2014, 04:11:21 PM
#23
lol I'm pretty sure you can't define x to be a natural number if we're trying to build them from scratch.


member
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April 05, 2014, 04:08:37 PM
#22
x being a natural ofc
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April 05, 2014, 04:06:24 PM
#21
what do we define X to be?

member
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April 05, 2014, 02:37:13 PM
#20
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...
full member
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April 05, 2014, 02:33:39 PM
#19
so what axioms do we use to define natural numbers?

What is the simplest one?
hero member
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Moonbet.io | Web3 Casino
April 05, 2014, 02:26:06 PM
#18
Maths is bore ! i didn't like to study math how can tell answer of this question very difficult to me
member
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April 05, 2014, 02:23:25 PM
#17
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
full member
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April 05, 2014, 02:00:38 PM
#16
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...





member
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April 05, 2014, 11:43:58 AM
#15
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
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April 05, 2014, 11:31:30 AM
#14
do you use the username "dankkk" when you're in JD or PD chat?

legendary
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You cannot kill love
April 03, 2014, 11:34:07 PM
#13
?
full member
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April 03, 2014, 06:18:00 PM
#12
dankkkk?

How's your 30+ loss streaks treatin ya?


legendary
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You cannot kill love
April 03, 2014, 04:51:56 PM
#11
ego and soul
hero member
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Will Bitcoin Rise Again to $60,000?
April 03, 2014, 04:48:21 PM
#10
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.
full member
Activity: 324
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April 03, 2014, 04:32:15 PM
#9
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.

full member
Activity: 196
Merit: 101
April 03, 2014, 04:21:49 PM
#8
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
full member
Activity: 324
Merit: 100
April 03, 2014, 03:37:50 PM
#7
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.
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