User blog:Bubby3/Linear Array Extended-Cascading-E notation.

I was impatiently watiting for Sbiis Saibian to publish his extension of Extended-Cascading-E notation (and all the pages on his site that say that they are on hiatus). He even said that he was going to return to working on his site in 2017. Now, 2017 is almost over and he still hasn't updated his site since February (when he posted his 2017 Renewal Plan). This is a ncase of broken promises. He promised to work on his site more in 2017, but in 2017 he was no more active on his site than he was in 2016. Because of his inablity to keep promises, I predict he will never update his site again.

Because of all of his inactivity, I plan on making my own fan extension to #xE^, which I will compare with his ad hoc extension. Here are some funermental sequences:

Fundemental sequence of {a,#,1,2} is a, a{a}a, a{a{a}a}a, ...

Fundemental seqeuence of {#,#,1,2}># is {#,#,1,2}, {{#,#,1,2},#,1,2}, {{{#,#,1,2},#,1,2},#,1,2}, ...

Fundemental seqeuence of {#,#,1,2}>(a+#) is {#,#,1,2}>a, {{#,#,1,2}>a,#,1,2}, {{{#,#,1,2}>a,#,1,2},#,1,2}, ...

Fundemental seqeuence of {#,##,1,2} is {#,#,1,2}, {#,#,1,2}>{#,#,1,2}, {#,#,1,2}>{#,#,1,2}>{#,#,1,2}, ...

Fundemental seqeuence of {a,b*#,1,2} is {a,b,1,2}, {a,b,1,2}>{a,b,1,2}, {a,b,1,2}>{a,b,1,2}>{a,b,1,2}, ...

Fundemental seqeuence of {a,#,2,2} is a, {a,a,1,2}, {a,{a,a,1,2},1,2}, {a,{a,{a,a,1,2},1,2},1,2}, ...

Fundemental seqeuence of {a,#,1,3} is a, {a,a,a,2}, {a,a,{a,a,a,2},2}, {a,a,{a,a,{a,a,a,2},2},2}, ...

Fundemental seqeuence of {a,#,1,1,2} is a, {a,a,a,a}, {a,a,a,{a,a,a,a}}, {a,a,a,{a,a,a,{a,a,a,a}}}, ...

Intution should fill in the rest.

Here is a comparison between my extension and Sbiis's ad-hoc extension.

{#,#,1,2}># = {#,#+1,1,2}

{#,#,1,2}>## = &(1)

{#,#,1,2}>### = &(#)

{#,##,1,2} = #*^#

{#,###,1,2} = #*^^#

{#,#,2,2} = #*^^^#

{#,#,1,3} = #*{#,#,1,2}#

{#,#,1,4} = #**{#,#,1,2}#

{#,#,1,#} = #*(#){#,#,1,2}#

{#,#,1,1,2} = #/^#

{#,#,1,1,3} = #//^#

{#,#,1,1,1,2} = #/x^#

{#,#,1,1,1,1,2} = #/xx^#

{#,#(1)2} = #(x^#)^# is at the limit of linear array notation, or the SVO