/sci/ - Science & Math » Thread #12668975

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Anonymous Fri 05 Feb 03:22:27 2021 No.12668975 View Reply Original Report

Quoted By: >>12668976 >>12668981 >>12668994 >>12669076 >>12669126

What the fuck is a number?

Anonymous

Anonymous Fri 05 Feb 2021 03:23:16 No.12668976 Report

Quoted By:

>>12668975
How much stuff's in stuffs

Anonymous

Anonymous Fri 05 Feb 2021 03:25:19 No.12668981 Report

Quoted By: >>12668985

>>12668975
a measure of magnitude of a quantity or frequency of objects in a given time and space

Anonymous

Anonymous Fri 05 Feb 2021 03:27:53 No.12668985 Report

Quoted By: >>12669006

>>12668981
You just know this guy thinks hes really smart

Anonymous

Anonymous Fri 05 Feb 2021 03:30:33 No.12668994 Report

Quoted By:

>>12668975
It’s like when you compare penis sizes but you don’t actually get to see the penises it’s just symbols on a paper describing how big they were

Anonymous

Anonymous Fri 05 Feb 2021 03:34:43 No.12669006 Report

Quoted By:

>>12668985
who doesn't on this fucking board. Regardless of whether he thinks hes smarter than he is, it is a pretty good answer to the question.

Anonymous

Anonymous Fri 05 Feb 2021 03:37:00 No.12669012 Report

Quoted By: >>12669071

Natural Numbers = Finite Set Cardinality
Integers = Diference between 2 Naturals
Rational Numbers = Ratio between 2 Integers
Real Number = Infinite Cauchy Series of Rational Numbers
Complex Numbers = All solutions to Quadratic Equations.
Quaternions = Pair of Complex Numbers.
Octornions = Pair of Quaternions.
...

Anonymous

Anonymous Fri 05 Feb 2021 04:00:51 No.12669071 Report

Quoted By: >>12669110 >>12669118 >>12669122 >>12669127 >>12669142 >>12669146

>>12669012
You don't know shit about extensions of $\mathbb{R}$ , do you?

Anonymous

Anonymous Fri 05 Feb 2021 04:03:57 No.12669076 Report

Quoted By:

>>12668975
a lingual concept used to describe orderly systems and logical operations

Anonymous

Anonymous Fri 05 Feb 2021 04:05:18 No.12669079 Report

Quoted By:

Depends on the number

Anonymous

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Anonymous Fri 05 Feb 2021 04:18:29 No.12669110 Report

Quoted By: >>12669118 >>12669122

>>12669071

Complex Numbers can be constructed as ordered pairs of Real numbers:

$(a,b)+(c,d) =(a+c,b+d)\\(a,b)\cdot (c,d) =(ac-bd,bc+ad).$

where $(a,b):=a+b\sqrt{-1}=a+ib$

I know that 4D Quaternions $(a,b,c,d):=a+ib+jc+kc$ , 8D Octonions and 16D Sedenions can be constructed in a similar way

https://en.wikipedia.org/wiki/Sedenion
https://en.wikipedia.org/wiki/Octonion
https://en.wikipedia.org/wiki/Quaternion

Anonymous

Anonymous Fri 05 Feb 2021 04:23:28 No.12669118 Report

Quoted By: >>12669122

>>12669071

>>12669110
Note: Fucking $\LaTeX$ compilation errors. God damn it.

Errata / Repost:

Complex Numbers can be constructed as ordered pairs of Real numbers:

$(a,b)+(c,d)=(a+c,b+d)$
$(a,b)?(c,d)=(ac?bd,bc+ad).$

where $(a,b):=a+b\sqrt{?1}=a+ib$

I know that 4D Quaternions
$(a,b,c,d):=a+ib+jc+kc$
, 8D Octonions and 16D Sedenions can be constructed in a similar way

https://en.wikipedia.org/wiki/Sedenion
https://en.wikipedia.org/wiki/Octonion
https://en.wikipedia.org/wiki/Quaternion

Anonymous

View Same Google iqdb SauceNAO Numbers.png, 30KiB, 562x492

Anonymous Fri 05 Feb 2021 04:26:31 No.12669122 Report

Quoted By: >>12669134 >>12669152

>>12669071

>>12669110 >>12669118
Note: Original posts deleted due to fucking $\LaTeX$ compilation errors.

Errata / Repost:

Complex Numbers can be constructed as ordered pairs of Real numbers:

$(a,b)+(c,d)=(a+c,b+d)$

$(a,b)?(c,d)=(ac?bd,bc+ad).$

where

$(a,b):=a+b\sqrt{?1}=a+ib$

I knowthat 4D Quaternions, ....

$(a,b,c,d):=a+ib+jc+kc$

..., 8D Octonions and 16D Sedenions can be constructed in a similar way

https://en.wikipedia.org/wiki/Sedenion
https://en.wikipedia.org/wiki/Octonion
https://en.wikipedia.org/wiki/Quaternion

Anonymous

Anonymous Fri 05 Feb 2021 04:27:40 No.12669126 Report

Quoted By:

>>12668975
Something about fingers idk

Anonymous

Anonymous Fri 05 Feb 2021 04:28:01 No.12669127 Report

Quoted By: >>12669134

>>12669071
Complex Numbers can be constructed as ordered pairs of Real numbers:
$(a,b)+(c,d)=(a+c,b+d)$

$(a,b)?(c,d)=(ac?bd,bc+ad).$

Anonymous

Anonymous Fri 05 Feb 2021 04:29:26 No.12669134 Report

Quoted By:

>>12669127 >>12669122
Why the fuck my $\LaTeX$ keeps compiling wrong on 4chan. God damn it.

Anonymous

Anonymous Fri 05 Feb 2021 04:30:35 No.12669142 Report

Quoted By: >>12669508

>>12669071
Complex Numbers can be constructed as ordered pairs of Real numbers:
$(a,b)+(c,d)=(a+c,b+d). \quad (a,b)\cdot(c,d)=(ac?bd,bc+ad)$

Anonymous

Anonymous Fri 05 Feb 2021 04:31:37 No.12669146 Report

Quoted By:

>>12669071
... where
$(a,b):=a+b\sqrt{?1}=a+ib$

Anonymous

Anonymous Fri 05 Feb 2021 04:32:39 No.12669148 Report

Quoted By:

... where
$(a,b) := a+b \sqrt{?1} = a+ib$

Anonymous

Anonymous Fri 05 Feb 2021 04:33:40 No.12669151 Report

Quoted By:

...I know that 4D Quaternions

$( a , b , c , d ) := a + ib + jc + kc$

Anonymous

Anonymous Fri 05 Feb 2021 04:33:45 No.12669152 Report

Quoted By: >>12669161 >>12669171

>>12669122
Congratulations, you can parrot wikipedia. There are lots of field extensions that can be constructed by pairing up reals but how do you specify the complex numbers? You don't know, and you don't know the differences between these algebras

Anonymous

Anonymous Fri 05 Feb 2021 04:34:41 No.12669156 Report

Quoted By:

..., 8D Octonions and 16D Sedenions can be constructed in a similar way

https://en.wikipedia.org/wiki/Sedenion
https://en.wikipedia.org/wiki/Octonion
https://en.wikipedia.org/wiki/Quaternion

Anonymous

Anonymous Fri 05 Feb 2021 04:35:22 No.12669157 Report

Quoted By:

At one level it is a form of eternal logic

Anonymous

Anonymous Fri 05 Feb 2021 04:36:59 No.12669161 Report

Quoted By: >>12669177

>>12669152
3 is not a lot.

Anonymous

Anonymous Fri 05 Feb 2021 04:39:55 No.12669171 Report

Quoted By: >>12669203

>>12669152
>parrot wikipedia

https://en.wikipedia.org/wiki/Complex_number#Formal_construction
"William Rowan Hamilton introduced the approach to define the set of complex numbers C as the set R2 of ordered pairs (a,b) "

Since then "Standing on the shoulders of giants" is a bad thing in /sci/ence?

I could parrot some random pdf book / lecture note or some random college professor. Would it be any different?

Anonymous

Anonymous Fri 05 Feb 2021 04:41:57 No.12669177 Report

Quoted By:

>>12669161
Fractal emergence

Anonymous

Anonymous Fri 05 Feb 2021 04:53:27 No.12669203 Report

Quoted By:

>>12669171
>Since then "Standing on the shoulders of giants" is a bad thing in /sci/ence?
Since *when *is "Standing on the shoulders of giants" a bad thing in /sci/ence?

Note: English isn't my 1st language.

Anonymous

Anonymous Fri 05 Feb 2021 05:00:34 No.12669224 Report

Quoted By:

The world of limits is an illusion

Anonymous

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Anonymous Fri 05 Feb 2021 07:12:59 No.12669508 Report

Quoted By:

>>12669142
$ \displaystyle a+ib \leftrightarrow \begin{bmatrix} a&-b \\ b&a \end{bmatrix} $

Anonymous

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Anonymous Fri 05 Feb 2021 10:24:48 No.12669793 Report

Quoted By:

I really like von Neumann's construction of naturals

Anonymous

Anonymous Fri 05 Feb 2021 10:32:47 No.12669806 Report

Quoted By: >>12670063

According to Frege's results in second-order logic numbers are a natural consequence of the concept of bijections. If you have bijections (called equinumerosity by Frege) you have the natural numbers.

Anonymous

Anonymous Fri 05 Feb 2021 12:02:55 No.12669966 Report

Quoted By:

output of counting function

Anonymous

Anonymous Fri 05 Feb 2021 12:51:50 No.12670063 Report

Quoted By:

>>12669806
Only if you assume classical logic. Equipotence classes are a hell in constructive logic, even for "finite" sets, disregarding the fact that there are a bazillion of different ways to be finite constructively.

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