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1. Consider the function f defined on the set of letters, where each letter is mapped to its position in the English alphabet (A=1, B=2, …, Z=26), and

f(x) = position(x) mod 2

- E is the 5th letter, so f(E) = 5 mod 2 = 1
- O is the 15th letter, so f(O) = 15 mod 2 = 1

Since f(E) = f(O), we conclude that E and O are equivalent under modulo 2.

2. Next, define a binary operation ⊕ on letters as:

x ⊕ y = (position(x) + position(y)) mod 10

- E ⊕ O = (5 + 15) mod 10 = 20 mod 10 = 0
- O ⊕ E = (15 + 5) mod 10 = 20 mod 10 = 0

This operation is commutative, as E ⊕ O = O ⊕ E.

3. Consider the identity element I under ⊕ as any letter L such that:

E ⊕ L = E

From step 2, 0 acts as the identity, showing that E and O behave identically with respect to ⊕.

4. By the properties of equivalence under modulo mapping and commutative operations, E and O are indistinguishable under these algebraic structures.

Therefore, within the framework of modular equivalence and the ⊕ operation, we conclude:

E = O

Zomphey u have been saying my letter

To update my page or to not update my page. The question remains, how many hours of my life do I want to waste?

The first edit of the Butterfly License is available for review. Note that there may be slight errors in it as its still WIP. I'd love to hear your thoughts in the comments on how I can improve it to be more universal and more protective to other creators. This is currently based on how I tend to release some of my content, so its definitely not tailored for everyone, but I try to make it the most large scale compatible as possible. It should easily cover all artistic creations, mods, code snippets, etc.

A basic summary, but that's just the tip of the iceberg when you only read this part.

Under 500xp before I'm level 10! :D

GUYS COUPLE NEW GUESS MY FAVE POLLS CHECK 'EM OUT:
www.sandboxgalaxy.com/forums/galaxy/discussion/guess-my-favorite-subject-school-education-job-etc-53/
www.sandboxgalaxy.com/forums/galaxy/discussion/guess-my-favorite-number-54/

Yayyyyy level 8!

Dude... How am i still 5 xp away from level 8.

i bet the moment i make this post I'm level 8...

Hi! If you wouldn't mind could you spam my non existent content

Some people here are levelling up like crazy

Okay, so... Since i play NONE of the games that are planets so far i can barely gain xp like everyone else because they likely play all the games here so it's EXTREMELY ANNOYING. So for that reason could anyone spam or whatnot that helps others gain xp so i could level somewhat like most of the other members even though i joined before the person literally 75 xp from level 10 and it just grinds at me. I'll return the favor to those who help me gain xp btw. Thx to anyone who kindly helps. :)

-Lego

Experimenting with enabling World Gen V2 on Hytale with a custom mod

So from what I've been able to figure out with Hytale world gen:

- There is a default world type
- That world type is built up of 4 zone types
- Each zone type has its own biomes

However I can't seem to modify the main world by changing zone 1, so maybe the seperate zone world types aren't the same as the ringed zones in the default world type?

Writing an initial review of Hytale, probably going to post it on here and on my website.