User blog:ArtismScrub/"Zoot notation": extending on the "zootzoot series"

See zootzoot, zootzootplex , zootzootzootplex , etc.

Wait, what even is this?
Basically, I figured out a way to extrapolate on the zootzoot, zootzootplex, etc.

zootzoot = googol!1

zootzootplex = googolplex!1

zootzootduplex = googolduplex!1

etc.

On the page where the numbers besides zootzootplex are named, Username95387 names up to zootzootdeciplex, and then:

zootzootzootplex = zootzootplex!1

That data can give the impression that:

zootzoot-x-plex = googol-x-plex!1

zootzootzoot-x-plex = zootzoot-x-plex!1

Which, in turn, can lead to:

zootzootzootzoot-x-plex = zootzootzoot-x-plex!1

zoot zoot zoot zoot zoot-x-plex =  zoot zoot zoot zoot-x-plex!1

...

(n "zoot"s)-x-plex = (n-1 "zoot"s)-x-plex!1

which can lead to a long series of extrapolation from the zootzootplex and its analogies.

I've recently thought of a way to denote these, creating kind of a series.

The Notation
So, here's what I've come up with:

Z(a,b) = (b "zoot"s)-a-plex

That means that:

zootzoot = Z(0,2)

zootzootplex = Z(1,2)

zootzootduplex = Z(2,2)

zootzootzootplex = Z(1,3)

and, in turn, many numbers can be coined beyond this.

For a technical definition of how the function works without mention of extrapolation:

Z(n,1) = E100#(n+1)

Z(n,x) = (Z(n,x-1))!1

Extension into higher-order googols
Yes, we can extend this into further means.

Let's say that:

Z(0,1,2) = 10↑↑100 (giggol )

Z(n,1,2) = 10 ↑↑(Z(n-1,1,2) (giggol-n-plex)

Z(n,x,2) = (Z(n,x-1,2)!2 (because !1 would be too weak on a pentational scale)

By means of name extrapolation:

Z(0,2,2) = zittzitt (analogous to "giggol")

Z(1,2,2) = zittzittplex

Z(2,2,2) = zittzittduplex

...

Z(0,3,2) = zittzittzitt

Z(1,3,2) = zittzittzittplex

etc.

Go one step further, to say:

Z(0,1,3) = 10↑↑ ↑ 100 (gaggol )

Z(n,1,3) = 10 ↑↑ ↑ (Z(n-1,1,3) (gaggol-n-plex)

 Z(n,x,3) = (Z(n,x-1,3)!3 (because !2 would be too weak on a hexational scale)



 So, again with extrapolation:

 Z(0,2,3) = zattzatt (analogous to "gaggol")

Z(1,2,3) = zattzattplex

Z(2,2,3) = zattzattduplex

...

Z(0,3,3) = zattzattzatt

Z(1,3,3) = zattzattzattplex

etc.



Continue this, such that...

Z(0,1,y) = 10{y} 100

Z(n,1,y) = 10{y} (Z(n-1,1,y) (gaggol-n-plex)

<p style="font-weight:normal;"> Z(n,x,y) = (Z(n,x-1,y)!y (where y still indicates a hyperfactorial)

<p style="font-weight:normal;">

<p style="font-weight:normal;"> Continue to say:

<p style="font-weight:normal;"> Z(0,2,4) = zeetzeet (analogous to "geegol")

<p style="font-weight:normal;">

<p style="font-weight:normal;">Z(1,2,4) = zeetzeetplex

<p style="font-weight:normal;"> Z(0,3,4) = zeetzeetzeet

<p style="font-weight:normal;"> Z(0,2,5) = zitzit (analogous to "gigol")

<p style="font-weight:normal;">

<p style="font-weight:normal;">Z(1,2,5) = zitzitplex

<p style="font-weight:normal;">

<p style="font-weight:normal;"> Z(0,3,5) = zitzitzit

<p style="font-weight:normal;"> Z(0,2,6) = zottzott (analogous to "goggol")

<p style="font-weight:normal;">

<p style="font-weight:normal;">Z(1,2,6) = zottzottplex

<p style="font-weight:normal;"> Z(0,3,6) = zottzottzott

<p style="font-weight:normal;"> Z(0,2,7) = zatzat (analogous to "gagol")

<p style="font-weight:normal;">

<p style="font-weight:normal;">Z(1,2,7) = zatzatplex

<p style="font-weight:normal;"> Z(0,3,7) = zatzatzat

<p style="font-weight:normal;">

<p style="font-weight:normal;"> Can we go further using the notation? Absolutely! But Bowers hasn't developed names for the primitive googol series beyond gagol, so we cannot name anything further than the zatzat series.

<p style="font-weight:normal;">Maybe Z(n,x,100) can coin us the wootwoot series, analogous to the woogol ? I don't know.

<p style="font-weight:normal;">I don't know what I could do for, say, a 4th entry or beyond, so I'll just leave it at this for now.