Gatedfinity (symbol: ⻔) is a number by Alesjif. It works based on a system of concepts, or GATEn, similar to many other locks.
Definition[]
Let n be any number or infinity.
GATE-1 is the limit of redlinkology.
GATE0 is the limit of numbers > 0. This can be described as Inv↓0.
GATE1 is the limit of calculation.
GATE2 is the limit of layers.
GATE3 is the limit of levels.
GATE4 is the limit of fields.
GATE5 is the limit of writing.
This goes on infinitely, every concept reaching a larger unit than the next.
GATEω0 is the limit of Itlogic.
The limit of this function, GATEL, can be described as Weak Gatedfinity.
Now, this is weak, so let's expand it.
Expansion[]
We can do GATEGATEn infinitely, so we will. GATEGATEGATE...n. This is still roughly GATEL. We can create GATEx,y to further expand this. x works like n, and y is the number of GATE's. GATEL is roughly GATEω,ω or GATEω[2]. Put a gate in that box, we get GATEω[GATEω]. Make this GATEω[ω,2]. The previous function would be GATEω[ω,0].
Then, this can contain a box. GATEω[ω[ω]]. Then, GATEω[ω[ω]] can be simplified to GATEω[[ω,2]], then GATE[[ω,3]]. Then, we can reach the limit of expansion, GATEωLE.
The number[]
The number is GATELLE. L in this calculation is the limit of the function, and LE is limit of expansion.