Leate_Wonceslace

Do you think a group isn't an algebra? What, by your definitions make an "Algebra" different from a "Ring"?

What the fuck are you talking about? That's incorrect as a matter of simple fact.

Associativity is a property possessed by a single operation, whereas distribution is a property possessed by pairs of operations. Non-associative algebras aren't even generally ones that posses multiple operations, so how the hell do you think one implies the other?

Edit: actually, while we're on it, your first comment was nonsense too; you don't know what an identity is and you think that there's no notion of inverses without an identity. While that's generally the case there are exceptions like in Latin Squares, which describe the Cayley Tables of finite algebras for which every element can be operated with some other element to produce any one target element. In this way we can formulate a notion of "division" without using an identity.

I appreciate your encouragement; it's an extremely rare occurrence when I discuss my ideas with others. I'll think about what you've said and if I follow through I hope to remember to send you a message. I'm favouriting this comment so I can find it again.

Correct; multiplying by Ω doesn't distribute over addition.

"Both sides are the same" is a queerphobic thing to say.

No, I'm pretty shy about my work in-person and I don't like linking my online and IRL self. Do you have any recommendations for places to put my work?

Someone else had the same observation, but it is unital. Keep in mind that it isn't associative; you can't pull out the Omega like that.

No; 1 is the multiplicative identity.

1Ω=Ω, and for all x in C 1x=x. Thus, 1 fulfills the definition of an identity.

underappreciated

They're literally the cause of most of our dedicated energy production infrastructure.

I highly recommend the book

No, I don't care.

I'm not evangelizing fossil fuels here

s u r e

This made me sad.

Okay, so I had a personal project for a long time that addressed the potential for an algebra that allowed for the multipicitive inverse of the additive identity.

In the context of the resulting non-associative algebra, 0/0=1, rather than 0.

For anyone wondering, the foundation goes as such: Ω0=1, Ωx=ΩΩ=Ω, x+Ω=Ω, Ω-Ω=Ω+Ω=0.

A fun consequence of this is the exponential function exp(x)=Σ((x^n)/n!) diverges at exp(Ω). Specifically you can reduce it to Σ(Ω), which when you try to evaluate it, you find that it evaluates to either 0 or Ω. This is particularly fitting, because e^x has a divergent limit at infinity. Specially, it approaches infinity when going towards the positive end and it approaches 0 when approaching the negative.

There's more cool things you can do with that, but I'll leave it there for now.

The democratic party is a coalition. It has wings that range from progressive to conservative. The reason they play it safe is because candidates need to be palatable to enough of the constituents to pass their primaries. This is also why local democratic parties are much more likely to have more cohesion.