/sci/ - Science & Math

>>12365858
For example, if our 0 is 0 in respect to positives and negatives, it could at the center in that picture.

The zero at the left is zero in respect to negatives and positive/negatives and the zero on the right is zero in respect to positive and negative/positives

Maybe infinity is defined as "having to start from 1 zero and go in a direction and to inifity but crossing at least 1 zero"
4 infinities and 3 zeroes.

>>12365893
or even better, it's defined by what zero it crosses, so that if two different infinities "cross" the same zero, they collapse in the same inifinity.
3 zeroes and 3 infinities. Oh yes my schizo mathematics is starting to please me

>>12365858
It's generally right, the distance from 0 to 0 is like distance from 0.9999 periodic to one and there are more of them.

However I guess if you write a paper about that nobody will be on your side.

>>12365899
Right, right.
But there are only 3 ways to approach 0, so there has to be 3 zeroes and 3 infinities.
-0.0000000000...1 to 0
0.00000000000...1 to 0
0 to 0

It wouldn't be too absurd to have 3 zeroes and 3 infinities

>>12365917
if 0 is neither positive nor negative, you could say that it's both there are 2 zeroes +-0 and -+0 approaching 0 itself

What if the two zeroes actually collapse to one zero to infinity, that's why there is a complete different mathematics hidden and we actually don't have to make it up but it exists in our mathematics already

-0.0000000000...1 to 0
0.00000000000...1 to 0

Basically if you have
0.999 periodic = 1
and -0.999 periodic = -1
but you can't do
0.00000 periodic without this being equal to 0 and there isn't a minimum
in regard to 0.000000...1,
Then you could literally make a new set of numbers +- -+

just to express ...
that does not lead to contraddiction,
to describe the minimum
0.00000...1 that would be the zero
and the minimum -0.00000...1 that would be another 0.
How do I publish this paper? it's so cool, can someone help me? I am not a researcher at all. I am just an Italian bored guy

>>12365960
expressing the "..."
as a quantity
aka, assigning that there is a minimum 0.000000000000...
and there is a minimum
-0.00000000000...
who both lead to the same inifity that collapses to 0 si REALLY cool, by the way my name is A.F. I am sardin#3529.
I have no idea if someone thought about this or if leads to contraddiction, I hope not.

This would allow to assign a value to anything
1.0000000000000...(1)
1.1000000000000...(1)
1.0000000000000...(-1)
1.1000000000000...(-1)
You would have the
-"infinitely tiny" or +"infinitely tiny"
regarding any number, so it would lead to thrice as much large set of numbers.

If you have whatever number, like 4, you could have 4 (-1), 4 and 4(+1)
here
(-1) and (+1) are the smallest unity possible.
they all relate to

0.0000000...
and
-0.000000...

Basically,
the smallest unity possible in the positives,
the largest unity possible in the negatives,

since you can't approach it from either way,

infinitely many smallest unities possible, make up the +0 on the right, they are so tiny that you need an inite of them to make a jump from
periodic 0.00000... = 0(at the center)
to

(0.00000...+0.0000...+0.0000... +n0.0000...) = 0(at the right)

since we never use 0.00000...
we always approach the 0 at the center directly, without approaching the 0 at the left or the 0 at the right.

>>12365923
Yeah, but then there are 3 if they both approach 0.
I didn't notice you wrote this, I thought I wrote this.
>>12365945
In fact I wrote this anticipating what you said.

btw I think this all schizo posting might work without contraddiction, I do not know if they ever thought about a unity infinitely tiny and how that unity requires to add itself infinite ttimes to collapse to the nearest complex number.

No one engages in my schizo talking.
Don't you find fishy there is a successor function only for natural numbers?
Come on JOOOOS

>posters: 2
3 now, I guess. What the fuck is the OP? Explain to me just the section in the image marked as "invisible realm of numbers".

>>12366058
If there's nothing between the two numbers, what stops you from adding them and dividing by two to make a number between them?

>>12366411
I was thinking if it's possible to make successors functions which generate a "successor" that is not exactly a number, obviously R is a dense order, but if you somehow can have a "unit" which given by an unary functor, like a function of successor S to a number r of R

just like in N you have
S(0), S((0)) ...to construct natural numbers,
you could have a successor function for reals to construct reals, but that "successor" is so tiny, infinitely tiny that it does not constitute a number because in R you have 0.0000... going to infinity, due to Σ_n c_n (1/10)^n

it's like if the cardinality of R is 2^ aliph0

The cardinality of this set of the functors constructing R, is a power set of R itself.
2^(2^aliph0)
it's like having a tiny unit for R, just like in N the unit is the successor function going from n to n+1,
it's the "1" of R
going from n of R, to n+0.000...1

between n and n+0.000...1 there is no number and n+0.000...1 is n itself as a number.
otherwise since it's a dense order this would lead to contraddiction.

Told you, schizotalk

This is just a mapping of tetration you schizo

It's a bit hard to understand you, but it sounds like you're talking about might be modeled by [math]\mathbb{R} \times \mathbb{Z}[/math] taken in lexicographic order; that is, (a, b) with [math]a \in \mathbb{R}, b \in \mathbb{Z}[/math] and taking (a, b) > (c, d) iff a > c or (a = c and b > d). Is that accurate? This only has cardinality [math]2^{\aleph_0}[/math], though.

This is a good starting point for understanding the kinds of things you can construct when you toss the Archimedean property:
https://en.wikipedia.org/wiki/Archimedean_group#Examples_of_non-Archimedean_groups

>>12366682
Oh yeah, this is very related thank you.

>>12366627
>mapping of tetration
yeah I can see that, a mapping of R itself, but as I said they aren't exactly numbers, they are infinitely small quantities, like the guy said I am trying to ditch Archimedean properties.
>>12366656
yeah I can see how the algebraic structure is left untouched then it's just a lexographic order onto R, but that would be lame.

I want a unit for R, infinitely small, that works like a successor function that discovers new things about limits =_= and hope that it shows how R is actually built, something Cantor missed. Come on JOOOSS

Fuck, they already did it and it doesn't lead to contradiction, it's iperreal numbers =_= a topologist just told me, well at least I don't feel extremely stupid

it uses a reciprocal of omega as infinitesimal small, I feel very stupid, I don't know why I haven't thought about it, well to be fair I have been thinking about this for 8 hours, but still =_________=

>>12366777
>>12366810
Hey bro don't fret. The fact that you came to many of these conclusions on your own is a sign that you have aptitude for the subject.

Build off of what you learned.

based schizo

>>12366836
thank you anon
>>12366873
yeah but at the end I had to give up the ideal of 3 0s even before realizing infinitely small unit exist

I don't know if now it's just a confirmation bias but basically there is a question of numerability and there seem to be a way that this is elementarily built from R

"However, a 2003 paper by Vladimir Kanovei and Saharon Shelah[4] shows that there is a definable, countably saturated (meaning ω-saturated, but not, of course, countable) elementary extension of the reals, which therefore has a good claim to the title of the hyperreal numbers. Furthermore, the field obtained by the ultrapower construction from the space of all real sequences, is unique up to isomorphism if one assumes the continuum hypothesis."

also, I am very stupid because when I thought
2^aliph0^aliph0 I didn't realize that
aliph0^aliph0= aliph0 so the cardinality =_= is the same, I thought that aliph0^aliph0 >aliph0
for some reason.
So yeah, it's not bigger but it is countably saturated

for some reason I was thinking about a "basic function" while a function is a subset of cartesian product, so the most "basic" structure is extinguishing intersections of nonempty sets, infact all functions are intersections of the cartesian product imho but not all intersections are functions.
So, even if the cardinality is the same the countability is saturated in that sense. By "expanding" R to hyperreals you still have the cardinality R.
I tried to read the paper but it's way above my league, I'll just leave it to the wiki reference

Sorry for bad English, it's pretty late desu

>>12367076
by numerability I meant countability*
https://en.wikipedia.org/wiki/Hyperreal_number
the quote is from this link
My alien waifu is giving me access to the shadow realm now, sayounara anons

https://web.archive.org/web/20040805172214/http://shelah.logic.at/files/825.pdf

For anyone interested, this is the paper, it's not impossible to read but still out of my league since I am just a schizo poster

>>12365917
It's not 1 at the end when you substract 0.999 from 1, because nines are infinite, you have number that's not 0, but it's distance from 0 to it it's 0, but it's right next to 0.

Pretty much like what I've got from your OP.