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pfr_4.png

Topic Operators

here are all the symbols which can be categorized by topics

01:Functions

Functions

Watch this first

If you have no idea what is a function, watch XR_XharpRazor talks about the basic concept of functions on our Learning Channel :

Defining a function

 

since a function takes an input and gives you an output, the glyph resembles a rectangle cup collecting the input and a triangle giving the output. In normal maths, when a function is declared, it is mentioned in words that a specific identifier is a function, here the symbol is used to specify that the identifier is a function.

​

here let's define the function "f(x) = 2x + 5" :

String Script

almost like in normal math, almost everything is the same,

it is just we need to add the "function definition" symbol

fct_01-def.png
121-f.png
opr_00-brk.png
Emoji_Circle_R.png
opr_00-brk.png
equ_01-equal.png
pfr_2.png
Emoji_Circle_R.png
opr_01-add.png
pfr_5.png

Story Board Script

Here, the input is written above the function identifier, and the output below.

Emoji_Circle_R.png
fct_01-def.png
121-f.png
pfr_2.png
Emoji_Circle_R.png
opr_01-add.png
pfr_5.png

Multiple inputs

a function can also have multiple inputs, such that each parameters need to be separated by comas

fct_01-def.png
fct_17-lerp.png
opr_00-brk.png
Emoji_Circle_R.png
sym_coma.png
Emoji_Circle_G.png
sym_coma.png
Emoji_Circle_B.png
opr_00-brk.png
equ_01-equal.png
opr_00-brk.png
Emoji_Circle_G.png
opr_02-sub.png
Emoji_Circle_R.png
opr_00-brk.png
Emoji_Circle_B.png
opr_01-add.png
Emoji_Circle_R.png

OR

Emoji_Circle_R.png
sym_coma.png
Emoji_Circle_G.png
sym_coma.png
Emoji_Circle_B.png
fct_01-def.png
fct_17-lerp.png
opr_00-brk.png
Emoji_Circle_G.png
opr_02-sub.png
Emoji_Circle_R.png
opr_00-brk.png
Emoji_Circle_B.png
opr_01-add.png
Emoji_Circle_R.png

What's this random function ?

​

The function above is a famous function "LERP", or linear-interpolation,

which is a function that takes a starting value, ending value, and a t-value, and it gives you a blend n between the 2 values.

Inverse

since the inverse is the total opposite of the original function, the glyph is just the function definition symbol flipped upside-down.

Emoji_Circle_R.png
fct_02-inv.png
121-f.png
opr_00-brk.png
Emoji_Circle_R.png
opr_02-sub.png
pfr_5.png
opr_00-brk.png
opr_04-div.png
pfr_2.png

Derivative & Integral

almost like the normal math we know, it is just the "d" from "dy/dx" has it's own symbol, the rest is just one to one substitution here.

fct_03-drv.png
fct_04-itg.png

derivative

integral

02:Geometry

Geometry

Geometry Components

Just like declaring a function, declaring a geometry component also requires the co-responding symbol to declare that the next identifier is a point/edge/surface/volume/mesh etc.

geo_00-dot.png
geo_01-line.png
geo_02-plane.png
geo_03-mesh.png

dot

(0D)

line

(1D)

surface

(2D)

mesh

(3D)

What is that symbol up there ?

It is one of the grammatical (/ fundamental) symbols that will be covered in future chapters.

Examples

declaring a dot "o" to be (0,0)

geo_00-dot.png
031-o.png
equ_01-equal.png
opr_00-brk.png
pfr_0.png
sym_coma.png
pfr_0.png
opr_00-brk.png

Geometry Relationships

Just like Equalities between numbers, geometry objects also has relationships, they behave like our normal math symbols : both operands are on both sides

geo_11-pdc.png

perpendicular

geo_12-prl.png

parallel

geo_13-sml.png

congruent

What is that symbol up there ?

It is one of the grammatical (/ fundamental) symbols that will be covered in future chapters.

Examples

saying "line A and line B are perpendicular"

geo_01-line.png
011-a.png
geo_11-pdc.png
geo_01-line.png
112-b.png

Trigonometry Functions

Just like a function, each function has their own symbols, all is left is the bracket with the input.

fct_11-sin.png
fct_12-cos.png
fct_13-tan.png
fct_21-asin.png
fct_22-acos.png
fct_23-atan.png

sin

cos

tan

asin

cos

atan

03:SetBool

Zoi - Set Theory & Boolean Aglebra

Why both together ?

turns out that both set theory and boolean algebra have connection in between them, they are somehow intertwined, and they are almost equivalent.

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.

set_ver2_01-def.png

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}"

set_ver2_01-def.png
Emoji_basket.png
equ_01-equal.png
opr_00-brk.png
Emoji_apple.png
sym_coma.png
Emoji_orange.png
sym_coma.png
Emoji_lemon.png
opr_00-brk.png

Predefined Sets

Some special sets has their own symbols

set_ver2_02-empty.png

empty set

[ zoi - no ]

set_ver2-03-uni.png

universal set

[ zoi - ni ]

set_ver2_04-pow.png

power set

[ zoi - næ ]

Set Relation

Just like numbers can have relations, sets and elements can also have relations.

set_ver2_11-belongTrue.png

is an element of

[ zoi - æru ]

set_ver2_12-belongFalse.png

is not an element of

[ zoi - æra ]

set_ver1_03-subsetTrue.png

is a subset of

[ zoi - ærui ]

set_ver1_04-subsetFalse.png

is not a subset of

[ zoi - ærai ]

Set & Boolean 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.

set_ver2-24-not.png

not

[zoi - rooo]

[ zoi - ro ]

set_ver2_21-or.png

union / or

[ zoi - riii ]

[ zoi - ri ]

set_ver2_23-sub.png

subtract

[ zoi - rioo ]

[ zoi - rio ]

set_ver2-25-xor.png

xor

[ zoi - rioi ]

set_ver2_22-and.png

intersect / and

[ zoi - roio ]

[zoi - royo]

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".

04:shortwords

Shortcut words

These symbols acts like substitutions of phrases, which can be helpful in proofing, documentation, etc

sym_because.png

because

sym_therefore.png

therefore

sym_forAll.png

for all

sym_thereExist.png

there exist

sym_given.png
sym_kosra.png

given that

Glyph Derivation

 

Some of the symbols are derived from some of the grammatic symbols, which will be covered in future chapters

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