jsfisher said:
It is a measurement unit. Really? You haven't used it as such. Did you really mean unit, like ohm are kilometer are units?
Exactly Cardinality, which is the measurement unit of the size (or magnitude) of existence.
jsfisher said:
Nope.
Cardinality 0 is the measurement unit of Emptiness, where Emptiness has no notation.
I believe that you have no problems to get the notion of the existing thing, called The empty set, where one of its notations is: {}.
By looking at {} you see that there is no notation to Emptiness (that is between "{" "}" ), nevertheless the measurement unit of Emptiness is Cardinality 0.
jsfisher said:
The number 0 is not a unit of anything; it is, well, a number.
Well, in this case, this number is the measurement unit of the existence (the cardinality) of Emptiness, where Emptiness has no notation (as shown above).
jsfisher said:
what does emptiness mean?
That has no predecessor, and Fullness is that has no successor, which its cardinality is
∞, and its notation is the outer "
{" "
}".
If only Emptiness and Fullness are considered, then the notation is:
{
}
jsfisher said:
Notation has never been a substitute for definition. Define first; you can notate later.
All done, the definition, the notation (or no notation), and the measurement unit (Cardinality) of the defined.
So, let's summarize:
You have failed to understand the definition of Emptiness and Fullness, and the measurement unit (Cardinality) of the defined.
Would an example help?
Cardinality is the measurement unit of Emptiness (that has no predecessor), Fullness (that has no successor) or that has predecessor AND successor.
Any thing that has predecessor AND successor, its cardinality > 0 and <
∞.
Some examples of things that have predecessor AND successor:
{
0 dimensional space, known as point and notated as {}, has measurement unit (cardinality) 1.
1 dimensional space, known as line and notated as {{}}, has measurement unit (cardinality) 2.
2 dimensional space, known as plane and notated as {{{}}}, has measurement unit (cardinality) 3.
...
In general, any n dimensional space, notated as {...{}...}, has measurement unit (cardinality) n+1.
...
∞ dimensional space, notated as ...{...}... , has non-strict measurement unit (cardinality).
}