My idea for a new notation.
A few days ago I was experimenting with a new type of notation that is similar to BEAF but at the same time is vastly different,
Define:
{a} = a.
{a,b} = a^b
{a,b,c} = a{b up arrows}c.
{a,b,c,d} = {a,b,c} recursed d-1 times.
To give an example of each of the 4 base levels we have:
{3} = 3.
{3,3} = 3^3 = 27.
{3,3,3} = 3{ 3 up arrows} 3 =
{3,3,3,3} = 3{(3{(3{3 up arrows}3) up arrows}3)up arrows}3.
To make this a bit clearer here is a brief explanation using letters and numbers.
Now that we have that defined we can move on to 5+ entry arrays.
{a,b,c,d,e} = {a,b,c,d} recursed ({a,b,c,d}-1) times for n>0.
Generally for an array of length k ( a k tuple) > 4 you recurse it ({k-1 tuple}-1) times.
Now lets move on to using the array of operator in my array notati…
The first official Googolism defined using my notation.
This is the first official googolism defined using my notation {3,7,3| 3,7#3} = Ternarygollumtree number.
I chose the name because it sounded kind of funny but also meaningful as gollum dies in the 3rd lotr book/film tree rhymes with 3 and Ternary is also related to the number 3.
Later on I hope to create a stronger notation using an original extension to a BEAF style array that can produce some pretty phenomenal results.
Array notation rule set.
Here is the rule set for my notation from: {a,b,c} to {a,b,c|d,k#p}
[a,1,c] = a+c
[a,2,c] = a*c
[a,b,c] = a{b-2}c if c > 2
[a,b,c|0] = [a,b,c]
[a,b,c|d] = [a,[a,b,c|d-1],c|d-1]
[a,b,c|d,0] = [a,b,c|d]
[a,b,c|d,e] = [a,b,c|[a,b,c|d,e-1]]
Now on to {a,b,c|d,k#p}
[a,b,c|@,0] = [a,b,c|@] (@ is any string)
[a,b,c|@,p,q] = [a,b,c|@,[a,b,c|@,p,q-1]]
Finally:
[a,b,c|d,k#p] = [a,b,c|(p d's),k]
So how do you think of that rule set.
Systematically creating the rule set of my notation.
After being away for quite a while from the wiki I decided to come back and try and create a better rule set for my notation starting at {a,b,c}.
I will first show them examples then develop a rule set from that.
{a,b,c} = {a (b-2 up arrows c}
for: b< 3 = a*b for b= 2 and a+b for b=1.
If b >= 3 apply the rule in line 1.
Now that I've got the rule set down for {a,b,c} I can start to give some examples:
{1,1,1} = 1+1 = 2.
{2,2,2} = 2*2 = 4.
{3,3,3} = 3^3 = 27.
{4,4,4} = 4(2 up arrows) 4.
{5,5,5} = 5( 3 up arrows) 5.
{6,6,6} = 6( 4 up arrows) 6.
{7,7,7} = 7(5 up arrows) 7.
{8,8,8} = 8(6 up arrows) 8.
{9,9,9} = 9(7 up arrows) 9.
{10,10,10} = 10(8 up arrows)10.
Now that I have given some examples I will write down a unique name for each of these examples:
{1,1…
what does everyone think about my array notation?
I have just been wondering what everyone thinks about my array notation , any suggestions to how I could improve it?