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
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.
Solar panels with attached energy storage like batteries or fly wheels.
Y'know, you could just admit that you're not paying attention. That's allowed.
It's not enough, but I've seen more of it from the DNC than I have you.
The US democratic party is a party of centrists with no goals
That's just not true. The democratic party is a coalition group with a great variety of goals that don't form a coherent ideal. You have AOC who's a either a social democrat saying she's a democratic socialist or a democratic socialist who's hiding her true ideals behind policies that advance her goals but are far easier to sell than what she really wants. Then you have obvious fascists who are clearly there only to enable the wealthy. Aside from them you have the people who believe that the democratic process is sacrosanct and above defiance even in the face of someone obviously attempting to subvert it.
Aside from that, on average the Democrats prefer action against climate change, that the rights of minorities be protected, and are less anti-worker than the GOP. These are real differences that matter. There's no such thing as "centrism" and pretending otherwise is an amazing way to excuse not supporting the largest institution that will lock your worst enemies out of power, even if they don't do anything.
Furthermore, even if the DNC literally never got anything done (which, to be clear, they have done good things that support workers like favorable rules for Unions)that would be great for us, because it'd mean their feckless ineffectual leadership would give us plenty of room to build parallel institutions, educate, and bring others around to our ways of thinking. When the GOP is in charge that becomes harder and it's more dangerous for everyone involved.
"Every previous president would have ended it by now."
"Biden literally couldn't do worse."
