Transfinite ordinals and large finite numbers

You know what, BEAF IS complicated to create in a basic language like Snap!. However, if you want to use it, don't copy, but analyze and create something from it if you plan to use it for the jam. (number at top is equal to tetradecal or {10,10,10,10})
Bowers Array Notation in Snap! script pic (5)

OK...Any alternatives?

I asked if there were any alternatives to BEAF. Is there, or no?

It's the kirby paris hydra, If you understand it, try to implement your own version of it (not exactly the same as it) and send it to the jam. Growth rate is actually quicker than BEAF and has a growth rate of F_(E0)(n)

image

Hold on, that reminds me of the TREE() function!

tree has a growth rate of SVO in FGH. However it is way more complex.

OMG!! THAT IS REALLY FAST GROWING! Hydra(4) is SOMEHOW greater than Graham's Number!?

Wait, what's "SVO in FGH"?

Fgh is fast growing hierarchy. What i mean by "SVO in FGH" is f_(θ(Ω^ω))(n)

So...what does that mean?

is kinda weird, like is the small omega symbol one of those transfinite numbers or somethin?

It's complicated, but it uses weiermann's function:
image

Yippee, more stuff incomprehensible to me.

It's not TREE(n) the function definition that's hard to define, it's the Kruskal tree theorem itself which is complicated.

Ok, so what are the G3(4 up arrows)3, tree(7)^tree(7)^tree(7)^tree(7)^tree(7)^tree(7)^8, and {3,6,3[1[1(weird thing)1,2]2]2} things? Also, how is the tree theorem complicated?

G3 = The graham function with input three, the arrows are Knuth up arrow, tree(7) is the weak tree function, and the last thing is an extension of BEAF.

Tree theorem definition
By the way it's a weaker version by Nash-Williams

Ok.

I was talking about the full thing, not the individual parts.

Yeah, but what's the weak tree function? and why is it raised to itself 5 times and then raised to the 8th power?

Ok, but how is that complicated, and what is the OG version?

I couldn't find the OG version.

G3^^^^3 = G3^^^G3^^^G3, which should be a very large number.