User blog:Googleaarex/5th item of ExE series

Here are all parts of ExE series:
 * 1) Hyper-E Notation
 * 2) Extended Hyper-E Notation
 * 3) Cascading-E Notation
 * 4) Extended Cascading-E Notation
 * 5) Extended Up-Arrow E Notation
 * 6) There is sub-items of this notation.
 * 7) Nested Up-Arrow E Notation
 * 8) Array Up-Arrow E Notation

Let \(E100\#\uparrow_{1}\#100 = E100\#\uparrow_{1}(100)100 = E100\#\uparrow^100\#100 = E100\#\underbrace{\uparrow\uparrow ... \uparrow\uparrow}_{100}\#100\).

Then \(E100(\#\uparrow_{1}\#)\uparrow_{1}\#100 = E100(\#\uparrow_{1}\#)\uparrow^100(\#\uparrow_{1}\#)100\), \(E100\#\uparrow_{1}\# > \#100 = E100\underbrace{((...(\#\uparrow_{1}\#)\uparrow_{1}\#)...)\uparrow_{1}\#)\uparrow_{1}\#}_{100}100\), etc.

There is \(\#\uparrow_{1}\#\# = \#\uparrow_{1}\# > ... > \#\uparrow_{1}\#\), \(\#\uparrow_{1}#\uparrow_{1}\# = \#\uparrow_{1}\#\underbrace{\uparrow\uparrow ... \uparrow\uparrow}_{\#}\#\), \(\#\uparrow_{1}\uparrow\# = \underbrace{\#\uparrow_{1}\# ... \#\uparrow_{1}\#}_{\#}\), \(\#\uparrow_{1}\uparrow_{1}\# = \#\uparrow_{1}\underbrace{\uparrow\uparrow ... \uparrow\uparrow}_{\#}\#\), \(\#\uparrow_{2}\# = \#\underbrace{\uparrow_{1}\uparrow_{1} ... \uparrow_{1}\uparrow_{1}}_{\#}\#\), etc.

Numbers

 * Googole = E100\#\uparrow\#100
 * Giggole = E100\#\uparrow\uparrow\#100
 * Gaggole = E100\#\uparrow\uparrow\uparrow\#100
 * Boogole = E100\#\uparrow_{\uparrow}\#100
 * Troogole = E100\#\uparrow_{\uparrow\uparrow}\#100
 * Superoogole = E100\#\uparrow_{\uparrow_{\uparrow}}\#100
 * Squaroogole = E100\#\uparrow_{\uparrow_{\uparrow\uparrow}}\#100
 * Toperoogole = E100\#\uparrow_{\uparrow_{\uparrow_{\uparrow}}}\#100
 * Poperoogole = E100\#\uparrow_{\uparrow_{\uparrow_{\uparrow_{\uparrow}}}}\#100
 * Omegeroogole = E100\#\uparrow_{,\uparrow}\#100
 * Duomegeroogole = E100\#\uparrow_{,\uparrow\uparrow}\#100
 * Ogigeroogole = E100\#\uparrow_{,,\uparrow}\#100
 * Osuperoogole = E100\#\uparrow_{,_{\uparrow}\uparrow}\#100
 * Finaloogole = E100\#\uparrow_{(|,_{1}\uparrow)\uparrow}\#100