/sci/ - Science & Math

that's not such a good diagram. maybe it should say "rational numbers" instead.

complex numbers
do matrices and tensors count cause they are collections of numbers and so are number-like

>>11666003
https://en.wikipedia.org/wiki/Surreal_number

>you now remember that Conway is ded

>>11666003
retard chart
theres way more irrationals than rationals

>>11666023
if it were proportionate then rational numbers wouldn't even be visible on the diagram since they have measure zero in the reals

>>11666003
Any unital real algebra can be thought of as an extension of the real number system. See the Cayley-Dickson construction for infinitely many examples.

>>11666023
>he wants a to-scale representation of an uncountably infinite set

>>11666023

>the size of the sector in a venn/euler diagram connotes the relative size of the sets

(see me!)

Image has some other semantic/graphic design problems; the irrationals and rationals partition the reals, so the image's visual suggestion (and here I put the lie to my above complaint, interpreting the graphical visually just as the other anon did) that the light purple sector is non-empty is false.

There is a "basic math" infochart which I've seen in many general stores over the years. It blithely states that since the axis (my word) of imaginary numbers and the axis of real number have no elements in common, they are disjoint. Woe betide the student who takes that one to heart.

>>11666003
Why are the whole numbers so much bigger than naturals, when the only difference is 0?

>>11666052
If the chart represented actual measure/cardinality, the naturals/integers/rationals would all be the same size, infinitely many invisible specks whose total size is zero, sprinkled in a sea of irrationals, which make up the reals.

Hey OP, you forgot the Gaussian integers. There are countably infinitely many different versions of them, one for each polynomial.

>>11666080
don't forget about p-adics

op is a brainlet retard highschool/calc student ruining this board

>>11666080
You mean rings of integers of finite extensions of the rationals. There is only one ring of Gaussian Integers.

>>11666003
quaternions are not a number, they are four numbers

>>11666003
So this is the largest or longest running conversation in mathematics? The ordering or sequence of what we actually utilize numbers for in a strict communication sense?

If numbers are genuinely some ideal being translated into the reals then how would a linguist describe this diagram in terms of source to destination via quotient argumentation?

Has to be some way to mathematically structure language so it is virtually zero-cost conjunctive exchange potential.

>>11666003
Wait.

What's an example of a real number, that is not rational and not irrational? The image indicates that some exist.

>>11666003
Learn abstract algebra, and you'll get a better understanding of your question.

>>11666003
p-adics
octonions
sedenions
ordinals
cardinals
nimbers
hyperreals
surreals

>>11666235
>What's an example of a real number, that is not rational and not irrational?

There are none, unless you want the law of the excluded middle to fail.

Op you should learn about ring theory. Despite the name it’s all about new number systems.

>>11666003
All sets that contain numbers beyond [math]\mathbb{R}[/math] are just extensions of [math]\mathbb{R}[/math] meant to serve some esoteric purpose, that [math]\mathbb{R}[/math] is not fit for.

[math]\mathbb{R}[/math] already contains numbers incredibly esoteric, like uncomputable and udefinable (in ZFC) numbers.

>>11666032
It can be to-scale when compared against the size of other infinite sets. It is known that some infinites are bigger than others.

>>11667970
>Watches a numberphile video once
I'd recommend checking out measure theory, it's a pretty interesting subject I've done intro while doing fun analysis, will continue this summer probably

>>11667970
hurr durr lets try to scale infinities against each other

this is your brain on po sincee

>>11666032
>>11668384
>>11668366
>thinking that an image, an IN-PERSON, DIRECT rePRESENTation, a literal specimen of the genuine article - THE HONORABLE SPACE AND TIME - in all of its COORDINATIVE, CINEMATIC GLORY, has LESS expressive power than the PITIFULLY INARTICULATE "entirety of known mathematics"
absolutely degenerate mathematics

>>11666003