/sci/ - Science & Math » Thread #13316508

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Please Explain

Anonymous Wed 23 Jun 23:23:00 2021 No.13316508 View Reply Original Report

Quoted By: >>13316517 >>13316659 >>13319209 >>13319214

Hi! I'm an absolute math beginner!
Can you kindly explain what are ring and set of numbers?
What is the usecase and why numbers are separated? Thank you! >-<

Anonymous

Anonymous Wed 23 Jun 2021 23:25:15 No.13316517 Report

Quoted By: >>13316529

>>13316508
>why numbers are separated?
clarify please, separated how?

Anonymous

Anonymous Wed 23 Jun 2021 23:28:21 No.13316529 Report

Quoted By: >>13316547 >>13316553

>>13316517
Separated by sets and rings...
People are very smart here and they seem to have a bigger understanding of math.
To me math is a set of rules (coming for programming) but some people have taken it too deep and they have a deep understanding of what math really is... How do I achieve this level? When I started programming, the first thing I learned is how the CPU works (data bus, stepper, Aritmetic-Logic unit, cache and so on...)
http://us.metamath.org/mpeuni/mmset.html#proofs This link is scary

Anonymous

Anonymous Wed 23 Jun 2021 23:31:29 No.13316547 Report

Quoted By:

>>13316529
>To me math is a set of rules (coming for programming) but some people have taken it too deep and they have a deep understanding of what math really is..
No your intuition is correct. Math is a fucking set of rules. If you want to "get" the entire big picture, read Paul Cohen's "Set Theory and the Continuum Hypothesis"

It's good that you have programming experience, this will be a quick read for you. You'll understand everything after reading this, and it's really easy reading.

Anonymous

Anonymous Wed 23 Jun 2021 23:33:15 No.13316553 Report

Quoted By: >>13316579

>>13316529
btw "math" is the stuff in plato's realm. Plato's realm is just the realm of all computer programs.

Anonymous

Anonymous Wed 23 Jun 2021 23:41:12 No.13316579 Report

Quoted By: >>13316616 >>13316632 >>13316906

>>13316553
Plato's philosophy asserts that there are two realms: the physical realm and the spiritual realm. The physical realm is the material stuff we see and interact with on a daily basis; this physical realm is changing and imperfect, as we know all too well.

This is the google definition.
How can math be the stuff in plato's realm if math by definition is a concrete, non changing thing?

Anonymous

Anonymous Wed 23 Jun 2021 23:56:27 No.13316616 Report

Quoted By: >>13316621 >>13317169

>>13316579
Well the positivist interpretation of Plato is just that the Platonic realm is just the realm of all computer programs. That's the 'idealized form'. The instances of these programs are when you have a map to nature.

The other Platonic stuff is just noticing the difference between "hardware" and "software", and also, it is noticing that WE ARE SOFTWARE, not hardware. As software, we are not tied down to one particular computing device (our body), but can be instantiated in different ways, including in a "perfect ideal way" (like a bug-free version of grep) in the heavenly abstract world of all computer programs.

I've never read plato, but I was importing the essence of his idea for the purposes of this thread. Read the cohen book.

Anonymous

Anonymous Wed 23 Jun 2021 23:58:20 No.13316621 Report

Quoted By:

>>13316616
I'll do. Thank you for your support.

Anonymous

Anonymous Thu 24 Jun 2021 00:01:33 No.13316632 Report

Quoted By:

>>13316579
The physical is a manifestation of the spiritual.
Matter is just a manifestation of Mind.

Checkmate, atheists.

Anonymous

Anonymous Thu 24 Jun 2021 00:14:10 No.13316659 Report

Quoted By:

>>13316508
Fuck off anime fag

El Arcón

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El Arcón Thu 24 Jun 2021 00:22:34 No.13316680 Report

Quoted By: >>13316686 >>13316689 >>13316869 >>13317161 >>13317178

A group is a like a closed monoid, which is basically a set with an operation. If it is closed, that means the output of the operation acting any of the elements in the monoid is still in the monoid. This is usually called a group and there are additive and multiplicative groups because the operation is usually addition or multiplication although the operation often denoted with "star" instead of "plus" or "times" because it could be anything. A ring is like a group with two operations: plus and times.

I think (1,2,3;+) is a monoid. It is a set {1,2,3} together with the addition operator. It is not closed because 2+3=5 and 5 is not in the set. When N is the set of all natural numbers, (N;+) is an additive group and (N;x) is a multiplicative group, (unless I am mistaken.) The sum of any two natural numbers is another natural number and so is the product of two natural numbers. The thing like (N;+,x) is where you start to define ring structure. It has a set in it, {N}, and also the plus and times operations.

El Arcón

El Arcón Thu 24 Jun 2021 00:25:17 No.13316686 Report

Quoted By: >>13316689 >>13316721

>>13316680
>the operation *is* often denoted with "star"
I forgot that all groups have inverses too so my examples with N are wrong nut they give you the broad idea.

El Arcón

El Arcón Thu 24 Jun 2021 00:26:50 No.13316689 Report

Quoted By:

>>13316680
>>13316686
And monoids differ from groups by not having inverses, not not having closure.

Anonymous

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Anonymous Thu 24 Jun 2021 00:40:30 No.13316721 Report

Quoted By: >>13316736 >>13316767

>>13316686
Could you refrain from using N as an abbreviation. Science and math is non-exclusionary and your obvious fragility and blatant dog-whistling is harmful to the collective pursuits here on the Science & Math board.
Now that this has been mentioned, I feel it would also be inappropriate to use n as well. Given the context, this could be your way of circumventing agreeable behavior. There are plenty of other letters you can use: i - for inclusive, j - jovial and friendly, k - well... you get the point. Remember, you made yourself that nigger guy. I don't know who hurt you, but only you can start the healing.

El Arcón

El Arcón Thu 24 Jun 2021 00:46:54 No.13316736 Report

Quoted By:

>>13316721
>Remember, you made yourself that nigger guy
Obviously anything that came of that interaction was the doing of the white man who filmed me calling him that and then uploaded it under false pretenses. The public perception of me was already much worse than what you say I have not suffered from it at all.

Anonymous

Anonymous Thu 24 Jun 2021 00:58:29 No.13316767 Report

Quoted By:

>>13316721
>, k - well... you get the point
sensible chuckle

Anonymous

Anonymous Thu 24 Jun 2021 01:36:01 No.13316852 Report

Quoted By:

Wow, a thread where Tooker of all people is the only one that attempts to give a useful answer to the OP. /sci/ is really amazing these days.

To OP: Roughly speaking, a set is a collection of object. We say that {1,2} is the set that contains the numbers 1 and 2. We write N=[1,2,3,4,...} for the set that denotes the positive integers. We write Z={0,-1,1,-2,2,...} for the set of all integers.
A ring is a set with additional algebraic structures. Roughly speaking, we want addition, subtraction and multiplication. For example,
Z is a ring with the operations + and -.

Why do we classify numbers this way. Because we can not only talk about numbers, but many many many different mathematical objects and many many different number systems that way.

Anonymous

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Anonymous Thu 24 Jun 2021 01:42:05 No.13316869 Report

Quoted By:

>>13316680
by this your saying that prime count supersedes natural causal count and were polluting our math skills with variables that could be much more conductive

Anonymous

Anonymous Thu 24 Jun 2021 01:57:39 No.13316906 Report

Quoted By:

>>13316579
> concrete
nope
> non changing
yep

Anonymous

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Anonymous Thu 24 Jun 2021 03:51:12 No.13317161 Report

Quoted By:

>>13316680
>A group is a like a closed monoid
Every magma is closed under the operation. A group is a monoid with inverses. https://www.youtube.com/watch?v=9OjWBjvpr4s

Anonymous

Anonymous Thu 24 Jun 2021 03:53:35 No.13317169 Report

Quoted By:

>>13316616
>Well the positivist interpretation of Plato is just that the Platonic realm is just the realm of all computer programs. That's the 'idealized form'. The instances of these programs are when you have a map to nature.
Retarded, all programming done by programmers is not working with Forms in any sense.

Anonymous

Anonymous Thu 24 Jun 2021 03:56:26 No.13317178 Report

Quoted By:

>>13316680
Hope you are doing well Tooker

Anonymous

Anonymous Thu 24 Jun 2021 17:12:11 No.13319209 Report

Quoted By:

>>13316508
A ring is a set of elements coupled with an addition operation and a multiplication operation. The elements need not be numbers; for example, they can be matrices. However, it's usually easiest to consider just numbers as the elements and work with those before moving on to more general elements.

Rings generalize fields. Fields are sets of numbers that come with addition and multiplication operations as well; the difference between rings and fields is that fields have multiplicative inverses and are commutative whereas rings lack either multiplicative inverses, commutativity, or both.

Anonymous

Anonymous Thu 24 Jun 2021 17:13:12 No.13319214 Report

Quoted By:

>>13316508
http://www-users.math.umn.edu/~brubaker/docs/152/152groups.pdf

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