Woo, I'm back and bring with me a cool upper/lower bound to a particular case in the fast growing hierarchy!

$$n\operatorname{Tet}(2^n,n,1)\le f_3(n)\le\operatorname{Tet}(2\sqrt[n]n,n,n)$$

where $$\operatorname{Tet}(a,b,c)=\underbrace{a\widehat{} a\widehat{}\dots\widehat{}a\widehat{}}_bc=\begin{cases}c, &b=0\\a\widehat{}\operatorname{Tet}(a,b-1,c) ,&b>0\end{cases}$$

(the little arrows are supposed to be exponent thingies)

Full proof

@user21820 @StevenH. you guys might be interested in the above.

@SimplyBeautifulArt If you are allowed to use LaTeX def, then you can define a new exponent operation symbol using \mathbin{^\wedge} or something like that, to make it auto-space as a binary operation.

Morning to all :3

@YokaiTheMonster Hello again! I'll be away for quite a while though.

yoo

@user21820 x'D :P Too lazy, just copy/paste all the way.

Haha..

=) How you like it?

Also, the little exponents look nicer on the main site

Haha too lazy to think through all that. =P

Well as far as form goes, I like it's simplicity and it's somewhat intuitive for me to think about f_3's growth rate

I see.

@XanderHenderson Here is a millennium falcon I was printing (unfortunately had to be abandoned midprint because filament spool was not spun correctly). As you can see it allows for fairly high detail (mine will print at a resolution of .6 mm/layer

I highly recommend getting one. You can print in different materials, PLA,SBA,Nylon, Polyesters etc

You can see how it would be fairly trivial to print lego blocks (which are made from ABS)

I'm addicted now

There are also tons of schems available for DIY that are fairly cheap

That is pretty nifty

as to grabbing models from the internets, and this is likely going to sound judgmental (though it is not meant that way), I feel that printing someone else's model is kind of a cop out

seems like it would be more fun to make one's own models

also, I AM HOME!

yay!