[ Zoiga ] - a Group/Set/Collection

Sometimes multiple individuals can be treated as a single entity

These words or concepts are used for multiple or a collection of nouns

The pronunciation is inspired by "Group", "Koi", "Zu"

01 : Declaring a set

02 : Predefined Sets

03 : Set Relations

04 : Noun Conjunctions

Declaring a set

Just like a function, there is a glyph used to declare a set,

here we also use a bracket with a coma-separated list to list out the content of the set.

define set

[ zoi - dæf ]

Glyph Derivation

The 2 circles resemble the Venn diagram, which is an important diagram in set theory.

All symbols that are within this category will have the "double circle" as its radical.

A set is a single circle, but why 2 ?

soon set operators will act on 2 sets, to make all the symbols more united, all set symbols will have the "double circle" radical.

Examples

declaring a set "basket" to be "{apple, orange, lemon}"

Predefined Sets

Some special sets has their own symbols

[ Zoi - Tæga - No ] [ ZoiTæNo ]

Empty Set

also can be translated into "nothing"

[ Zoi - Tæga - Na ] [ ZoiTæNa ]

Universal Set

also can be translated as "all", "everything"

[ Zoi - Tæga - Næ ] [ ZoiTæNæ ]

Power set

so far there is no "normal conversation translations"

Set Relations

Here, these words can be treated as a group of verbs

these verbs are used to describe if an entity / group belongs to a collection or a category.

[ Zoi - æru ]

is an element of

[ Zoi - æra ]

is not an element of

[ Zoi - ærui ]

is a subset of

[ Zoi - ærai ]

is not a subset of

Examples

here are a few examples using these words :

[ KoiNi ] : "me"/"I"

[ Zoi-æru ] : "is an element of "

[ Særia-Klari ] : "Source - Creation" , "Creator"

[ KoiXoNya ] : "Cat"

[ KoiNi Zoi-æru Zoi Svæk Særia-Klari Svok ] : "I am a Creator"

[ KoiNi Zoi-æra Zoi Svæk KoiXoNya Svok ] : "I am not a Cat"

note : there are many different ways to say the same thing

Group Conjunctions and Operations

These are the operations you can run on sets, under some circumstances, they also work on booleans. In this case, they behave like how we are familiar with set and boolean operations in normal math.

not

[zoi - rooo]

[ zoi - ro ]

[ Zo ]

union / or

[ zoi - riii ]

[ zoi - ri ]

[ Zi ]

subtract

[ zoi - rioo ]

[ zoi - rio ]

[ Zio ]

xor

[ zoi - rioi ]

[ Zioi ]

intersect / and

[ zoi - roio ]

[zoi - royo]

[ Zoio ]

The Connection between Set and Boolean

First let's take a look at how does the union operator works :

"A union B" can be interpret as "if you are in set A OR set B, you will be selected"

the selected elements will need to be in A OR B, and this is why the set operator "union" is also a boolean operator "or".

If the sentence is simple enough such that we do not end up with ambiguity, then these are enough, otherwise, extra parts are required.

sometimes to avoid ambiguity, some operator will have a "left side", "separator" and "right side"

here we have the side by side compariso.

not A

A or B

A xor B

A and B

The left side is pronounced as [ (X)-ræ ] , the separator is [ (X)-ro ] and the right side is [ (X)-ra ]

where (X) is either [ Zo ] or [ Zi ] or [ Zioi ] or [ Zoio ]

sometimes, if we have a list of entities that are clumped in the same list and the same operator, an operator can have more than 2 arguments :

A or B or C or D

here, arguments can be another operation, this means that we can keep nesting.

we are rewarded with concise, but trading with wordiness

if a clump only has 2 entities, then that clump don't need a left side and a right side, and it will act as a separator, however, giving them a left side and right side is optional here, not prohibited.

The main idea here is "Left side and right side can be added to avoid ambiguity"

( ( A or B ) and ( C xor D ) )

[ ZoioRæ ZiRæ A ZiRo B ZiRa ZoioRo ZioiRæ C ZioiRo D ZioiRa ZoioRa ]

[ ZoioRæ A Zi B ZoioRo C Zioi D ZoioRa ]

There is no order of operation, the order can only be determined by the nesting structure.