Recent content by eddybob123

Maybe it's to avoid Aaronson #9. Quoted directly from his blog: But when it comes to something like P≠NP, to “motivate” your result is to insult your readers’ intelligence.

Re: Prove: 1^3+3^3+5^3+7^3+...+T^3= Someone else can finish this off. I stopped trying. (Tongueout)

So what you're saying is... addition is distributive over multiplication. (Bandit)

I am not assuming any of those things. If an operation is distributive and associative, then isn't it automatically closed? This is what forms rings from abelian groups.

The operations $+$ and $\cdot$ are intended to be less abstract. Yes, $+$ need not be closed over $G\cup H$, but is it required $\cdot$ is closed over it? In your first post of this thread, it seems as though you have misunderstood my question. Obviously, there is only one non-isomorphic monoid...

Then is it a semigroup?

Suppose that $(G,+)$ and $(H,+)$ are both monoids and that the operation $\cdot$ is closed, associative, and distributive over $+$ in $G$ and $H$. My question then is whether or not $(G\cup H,\cdot)$ is necessarily a monoid. I have evidence to suggest that it might, though I cannot prove it.

Re: Solve in positive integers for a^2=9555^2+c^2

The OP never asked for specific numbers.

Not to mention: $$\varphi =1+\frac{1}{1+\frac{1}{1+\frac{1}{1+...}}}$$ $$\sqrt{2}=1+\frac{1}{2+\frac{1}{2+\frac{1}{2+...}}}$$ $$e=2+\frac{1}{1+\frac{1}{2+\frac{1}{1+...}}}=[2;1,2,1,1,4,1,1,6,1,1,8,...]$$

Re: Challenge (Clapping)

There are 10 types of people in the world: those who understand base 16, and F the rest. (Tongueout)

Fraction:$\frac{187465}{6744582}$ Continued fraction: $[0,35,1,44,111,2,2,12,4]$ Unit fraction expansion: $\frac{1}{36}+\frac{1}{58395}+\frac{1}{9724688047}+\frac{1}{283708672824669334580}$