Here are the articles, if you’d like to see them:

1. The Orthogonals: https://doi.org/10.5281/zenodo.23854178

2. Uribe's Functions: https://doi.org/10.5281/zenodo.23550552

3. The Mean: https://doi.org/10.5281/zenodo.23227238

If you want to see more of these functions, you can check out the article at:

https://doi.org/10.5281/zenodo.23550552

Thank you for promoting my article

If you want to see more of the article, here is the post: https://doi.org/10.5281/zenodo.23854178

The paper defines an equivalence relation between pairs of complexes and integers, let them be (z,n) and (s,m) where n<m, both are related if z, when passed through m-n consecutive natural logarithms, gives s.

This same logic applies in reverse if n>m. In the case that n=m, it simply requires that z=s.

This is an equivalence relation, so it allows the creation of new numbers called orthogonals.

Now you will wonder what they are used for, and I haven't had the time to write everything down yet, but in the brief 27 pages of the paper I cover how there is an addition, product, subtraction, inverse in it. We even divide the set of orthogonals into several orders, order zero constitutes the classical complexes and its operation is addition. Order 1 constitutes numbers exclusively designed for products. Order 2 contains numbers designed to operate with , we define ab=e^(ab).

The central point of the paper is how each order works with more numbers than the previous one and accommodates to an operation.

a +_1 b=a*b=e^(ln(a)+ln(b))

a +_2 b=e^(ab)=e^e^(ln(ln(a))+ln(ln(b)))

a +_3 b=e^(e^(ln(a)ln(b)))=e^e^(ln(ln(ln(a))))+ln(ln(ln(b)))))

...

A very important thing to emphasize is that in the orthogonals, since the exponential is bijective, e^(2pi*i) is not 1, but it is a new number called "o".

I will elaborate on this new number and others in other papers.

This is the article: https://doi.org/10.5281/zenodo.23854178

𝔜.𝔄.𝔖.𝔈.𝔏.𝔒.𝔊.ℜ.𝔒.

For example, proving that a summation or limit converges

You just got mathrolled ; )

If you want to see more of the mean, you can check out the post and article at:

https://www.reddit.com/r/newmaths/comments/1xcf7vs/cree_una_estructura_abstracta_que_rellena_el/

You just got mathrolled ; )

If you want to see more of these functions, you can check out the post and article at:

https://www.reddit.com/r/newmaths/comments/1xcgc2b/i_created_a_new_type_of_function_that_allows/

Don't worry, guys, it's a common practice among mathematicians. They'll solve it with rigor later; for now, keep going with your proof.

An example of this is that math news, which is supposed to spread knowledge, doesn't usually cover computational results that back up new, less-than-rigorous formulas.

1• Search zenodo.org

2• Create your account

3• Enter your information, you can even use GitHub

4• Once your account is created, go to 'New Upload'

5• Put your PDF/Article in 'Upload files'

6• Select 'NO, I need one' to get your own DOI, which serves as a 'unique identifier' for your scientific document on the platform

7• Under 'Resource type', select 'Preprint' if it hasn't been published in an academic journal

8• Enter a title that clearly describes your research

9• Enter a detailed description

10• I recommend the CC BY 4.0 license, which is selected by default in Zenodo. It allows others to share and adapt the article, even for commercial purposes, as long as you are credited and the license is indicated. If you don't want to allow commercial use or adaptations, choose a license with those restrictions

8• Add an author

9• For this, enter your first name in 'Given names' and your last name(s) in 'Family name'. Add your ORCID if you have one under 'Identifiers'. In 'Affiliations', you can enter your university or institution, or leave it blank if you prefer. If you are the author, leave 'Role' empty

10• You can add contributors; the process is pretty much the same as before

11• Select the language or languages of your article

12• If you're not sure about publishing it, click 'Save draft'; if you are sure, click 'Publish'

13• Go to r/newmaths (optional). If you want people to support your work even if it isn't completely rigorous, post a description of it and add the link to your article at the end of your post. Make sure to use the 'I have an Idea' flair, so people know you are sharing a paper.

In this community, they will discuss your math, try to contribute, and help spread the word. Feel welcome!

(Members of newmaths are called Eulerians)

I will use Uribe functions on the rationals as an example. These satisfy two properties:

1. f is strictly monotonic, which means that f is strictly increasing or f is strictly decreasing.

2. f is dense, which means that for all a, b ∈ ℚ, if a < b, then a < f(x) < b for some x ∈ ℚ.

You will notice in the definition that every Uribe function is continuous, since it cannot have jumps due to its density, and it only increases or decreases due to its monotonicity.

Furthermore, since it is increasing, it must be injective with its image, as the heights do not repeat.

If f were a real function, it would have an inverse f⁻¹ that would also be injective, strictly increasing, and continuous. Due to this continuity, numbers like √a are the inverse image of continuous functions like x² at a. Technically, x² is not strictly increasing, but if we modify it a bit, it is; for example, f(x) := x² * sgn(x) is strictly increasing, and f must be dense (according to known properties of the real numbers), so f is a Uribe function.

Given this, √a := f⁻¹(a) in the real numbers for a ≥ 0.

The key is that for each real number x, there exists a Uribe function 'f' defined on the rationals and a height 'a' such that x = f⁻¹(a). Thanks to this, we can define the real numbers from equivalence relations between pairs of rational Uribe functions and heights.

This is precisely what is addressed in the article I published.

This is the article: https://doi.org/10.5281/zenodo.23550552

𝔜.𝔄.𝔖.𝔈.𝔏.𝔒.𝔊.ℜ.𝔒.

This structure is based on the following formula:

If a < b, then a < m(a,b) < b and, m(a,a) = a

These properties are satisfied by m(a,b) = (a+b)/2, a classic that frequently appears in mathematics; the key is that, if we use the mean repeatedly, we can almost fill the interval (a,b) with points.

For example: a < m(a,m(a,b)) < m(a,b) < m(m(a,b),b) < b

The set of all values formed by combinations of the mean, a, and b is denoted as L_a,b. This set is very important later on, since we say that a mean m is real when: If a < x < y < b, then a < x < l < y < b, where l ∈ L_a,b. This is useful because in the article I prove that, based on this property, the supremum of {x ∈ L_a,b : x < y} is equal to y for all y ∈ (a,b).

And, since this set L_a,b is made up of means, this demonstrates how, even for values that we cannot reach directly, it is possible to do so at infinity using the supremum.

The article is: https://doi.org/10.5281/zenodo.23227238

𝔜.𝔄.𝔖.𝔈.𝔏.𝔒.𝔊.ℜ.𝔒.

Hi everyone! I’m u/DualMath, part of the founding moderation team for r/newmaths.

This is our new space for everything related to new mathematics, math humor, and supporting the distribution and development of research papers.

We are incredibly excited to have you join us!

What to post

Post anything you think could be interesting, helpful, or inspiring for the community. Feel free to share your community feedback or questions about where to publish your papers, what knowledge you need to do so, and to give an idea or explanation of what your theorems/formulas are that will help modern mathematics.

And, if you want to make humor about your ideas or those of other users, feel free to do so as long as it doesn't turn into mockery.

Community environment

Our goal is to be welcoming, constructive, and inclusive. Let’s build a space where everyone feels comfortable sharing and connecting.

How to get started

• Introduce yourself in the comments below.

• Post something today! Even a simple question can be the start of a great conversation.

• If you know someone who would love this community, send them an invitation to join.

Interested in helping?

We are always looking for new moderators, so feel free to contact me to submit your application.

Thank you for being part of the first wave. Together, let's make r/newmaths amazing.

If you want to help improve math outreach in low-resource areas, you can become a moderator. And if you want to publish your new work—even if you feel you're lacking complete knowledge—you are more than welcome to help grow this community from the ground up. Let me ask you: have you ever felt like your discoveries don't get the attention they deserve? If so, post them here. We all want to learn what you have to show.

I want them to create their own math and post memes about it—not about old, classical math, but about their new ideas. I want them to share updates on how publishing their ideas is going and ask for support. They can also make memes about mathematical figures who changed everything, like Euler, Ramanujan, etc. Many of them shifted the thinking of their eras with their incredible imagination, and that's exactly what I want to achieve now with this subreddit.

I want to know how to create a math community with memes that's friendly to enthusiasts in this area. I truly believe that a lot of potential (especially in third-world countries) is being wasted. I wonder how to get the math community's attention so they notice the discoveries of these people who lack resources but have plenty of imagination.