User:Googleaarex/Hyphen Notation Part 1

Part 1 of Hyphen Notation

Extension 0 (Original)
1. a-b = a^b

2. a-1-c = a

3. a-b-c = a-(a-(b-1)-c)-(c-1)

Extension 1
4. #-a-b = #-(#-(a-1)-b)-(b-1), where # is any array.

The limit of this extension is a-b-c-...-x-y-z.

Extension 2
5. #-a---...---b = #-a---...--a ... a---...--a with b a's

The limit of this extension is a---...---b.

Extension 3
a-^-b = a---...---a with b bars

a-^--b = a-^-a-^-a...a-^-a-^-a with b a-^-a's

a-^-^-b = a-^---...---a with b bars

a-^^-b = a-^-^-^-...-^-^-^-a with b -^'s

a-^^--b = a-^^-a-^^-a...a-^^-a-^^-a with b a-^^-a's

a-^^-^-b = a-^^---...---a with b bars

a-^^-^^-b = a-^^-^-^-^-...-^-^-^-a with b -^'s

a-^^^-b = a-^^-^^-^^-...-^^-^^-^^-a with b -^^'s

The limit of this extension is a-^^^...^^^-b.

Extension 4
a-^*-b = a-^^^...^^^-a with b ^'s

a-^*-^*-b = a-^*-^^^...^^^-a with b ^'s

a-^*^-b = a-^*-^*-^*-...-^*-^*-^*-a with b -^*'s

a-^*^*-b = a-^*^^^...^^^-a with b ^'s

a-^**-b = a-^*^*^*...^*^*^*-a with b ^*'s

a-^**^**-b = a-^**^*^*^*...^*^*^*-a with b ^*'s

a-^***-b = a-^**^**^**...^**^**^**-a with b ^**'s

a-^*(^)*-b = a^***...***-a with b *'s

a-^*(^)**-b = a-^*(^)*^*(^)*^*(^)*...^*(^)*^*(^)*^*(^)*-a with b ^*(^)*'s

a-^*(^)*(^)*-b = a-^*(^)***...***-a with b *'s

a-^*(^^)*-b = a-^*(^)*(^)*(^)*...*(^)*(^)*(^)*-a with b (^)'s

a-^*(^^)*(^^)*-b = ^*(^^)*(^)*(^)*(^)*...*(^)*(^)*(^)*-a with b (^)'s

a-^*(^^^)*-b = a-^^*(^^)*(^^)*(^^)*...*(^^)*(^^)*(^^)*-a with b (^^)'s

etc.

The limit of this extension is a-^*(^*(^*(...(^*(^*(^*(^)*)*)*)...)*)*)*-b.

Extension 5
a-^'-b = a-^*(^*(^*(...(^*(^*(^*(^)*)*)*)...)*)*)*-a with b levels

a-^'^-b is next level.

We can have a-^'^^-b, a-^'^^^-b, etc.

Also a-^'^*-b, a-^'^**-b, etc.

Then:

a-^'^'-b = a-^'^*(^*(^*(...(^*(^*(^*(^)*)*)*)...)*)*)*-a with b levels

a-^'*-b = a^'^'^'...'^'^'^'-a with b levels

etc.

Then:

a-^''-b = a-^'*(^*(^*(...(^*(^*(^*(^)*)*)*)...)*)*)*-a with b levels

This makes a visible pattern.

The limit of this extension is a-^'(^'(^'(...(^'(^'(^')')')...)')')'-b.

Extension 6
Let define * is {^} and ' is {^^}.

The limit of this extension is a-^{^{^{...^{^{^}}...}}}-b.

Extension 7
Let define a-(-)-b = a-^{^{^{...^{^{^}}...}}}-a /w b nested

Define a-(-)--b = a-^{-^{-^{...-^{-^{-^-(-)-}-(-)-}-(-)-...}-(-)-}-(-)-}-(-)-a /w b nested

Define a-(-)^-b = a-(-)-(-)-(-)...(-)-(-)-(-)-a /w b (-)'s

Define a-(-)^^-b = a-(-)^-(-)^-(-)^...(-)^-(-)^-(-)^-a /w b (-)'s

Define a-(-)^*-b = a-(-)^^^...^^^-a /w b ^'s

Define a-(-)^'-b = a-(-)^*((-)^*(...(-)^*((-)^*)...))-a /w b nested

Define a-(-)(-)-b = a-(-)^{(-)^{(-)^{...(-)^{(-)^{(-)^}}...}}}-a /w b nested

Define a-(--)-b = a-(-)(-)(-)...(-)(-)(-)-a /w b (-)'s

Define a-(-^-)-b = a-(---...---)-a /w b -'s

The limit of this extension is a-(-(-(...-(-(-)-)-...)-)-)-b.

Extension 8
a-((-))-b = a-(-(-(...-(-(-)-)-...)-)-)-a /w b nested

a-((-))--b = a-(-(-(...-(-(-((-))-)-((-))-)-((-))-...)-((-))-)-((-))-)-((-))-a /w b nested

a-((-)-)-b = a-((-))((-))((-))...((-))((-))((-))-a /w b ((-))'s

a-((-)--)-b = a-((-)-)((-)-)((-)-)...((-)-)((-)-)((-)-)-a /w b ((-))'s

a-((-)(-))-b = a-((-)-((-)-(...(-)-((-)-((-)-)-)-...)-)-)-a /w b nested

a-((--))-b = a-((-)(-)(-)...(-)(-)(-))-a /w b (-)'s

a-(((-)))-b = a-((-((-((...-((-((-))-))-...))-))-))-a /w b nested

The limit of this extension is a-(((...(((-)))...)))-b.

Extension 9
Let a-(-)0-b be a-b, a-(-)--b be a-(-)-b, a-(-)---b be a-((-))-b, etc.

The limit of this extension is a-(-)-(-) -(-) ... -(-) -(-) -(-) 0- - - ... - - -b.