see googolisms constructible HERE
The notation is an inprogress. For now I'll show examples
E100{a,b,c,...,#,#,#...,#,#,#}100 (note, exactly # entries) = E100{#,#(1)2;a,b,c,...}100
E100{#,#(1)2}>#100 = E100{#,#(1)2;#,#+1}100
E100{#,#(1)2}>{#,#(1)2}100 = E100{#,#(1)2;#,#+#}100
now here E100{#,#(1)2}>{#,#(1)2}>...(99 >s)...>{#,#(1)2}>{#,#(1)2}100 (hectastaculated-ominongulus) is NOT equal to E100{#,##(1)2}100 (ominongulcross). heck its much bigger! notice here hectastaculated-ominongulus still has ONLY # ENTRIES, while ominongulcross by definition has ## entries. thus they are DEFINITELY NOT DIFFERENT. (SEE GLOLN PART 6)
That's why I created this notation. an intermediate of ##xE^, {}xE^, :xE^, etc where there's a gap.
I call this "Punctuation-Extended Cascading-E notation" or ;xE^ for short, from the first punctuation mark used here.
Now what happens when we reach E100{#,#,#,#,#,...,{#,#,#,#,...,#}}100 ? Well we will just use the punctuation mark I used in the last sentence, the question mark. so E100{#,#,#,#,#,...,{#,#,#,#,...,#}}100 = E100{#,#(1)2;?{#,#(1)2}}100
Now we would reach E100{#,#,1,1,1,...,1,1,1,2}100 and this time with #+1 entries.
I called this E100{#,#¤2}100.
rules of using ¤:
(note! I'm gonna be using letters for rules to represent delimiters, eg 1, 2, #, {#,#(1)2}, etc,)
{base,prime¤2} = {base,base(1)2;?{base,base(1)2;?... (prime-1)*2 "base"... }} = {base,prime,1,1,1,...,1,1,1,2}
{a,b,c,...,n,1¤z} = {a,b,c,...,n¤z}
{a,1,b,...,n¤z} = {a,1¤z}
{a,b,1,...,1,c,d,...,n¤z} = {a,a,a,...,{a,b-1,1,...,c,d,...,n},c-1,d,...,n¤z}
If rules 1-4 don't apply:
{a,b,c,d,...,n¤z} = {a,{a,b-1,c,d,...,n},c-1,d,...,n¤z}
If rules 1-5 don't apply:
{a,b¤z} = {a,a,a,... b a's...,a,a,a¤z-1}
Similar to rules of BEAF right.
lastly I have a & function and actually thats there in ##xE^ too.
{#&#} = {#,#(1)2}
{(#+1)&#} = {#,#(1)#} (in my pxec atleast!)
{##&#} = {#,#(2)2}
{#^#&#} = {#,#(#)2}
{#^^#&#} = {#,#(#^^#)2}
{3&#&#} = {#,#({#,#,#})2}
...
Now let's forge onto a bunch of numbers we can coin with the notation!! NEXT ->