Note that the only canonical appearances of Algebralians are from Battle for Dream Island. Their appearances in the pre-BFDI comics and XFOHV are considered not canon, meaning they are not part of the central universe and timeline of events.
Integers are based upon numeric digits. Numbers made their debut in "X Finds Out His Value", with One, Three, Four, Five, Six, Seven, and Eight making their first appearances. In its spiritual successor, "The Number Playground Chronicle!", Two, Zero, and Nine are introduced. In "Thanks for 1,000,000 subscribers!", Ten is introduced.
Variables are based upon mathematical variables. Most use or are represented by letters in the Latin alphabet. X was introduced in "X Finds Out His Value" as the very first variable, with N Variable, Y Variable, and Z Variable being introduced in "The Number Playground Chronicle!".
Polygons were introduced in "The Number Playground Chronicle!". They are based upon the first 10 polygons by sides minus heptagon (7 sides). They did not make any more appearances after their debut.
Irrationals were introduced in "The Number Playground Chronicle!". One member, Pi Irrational, served as a journalist and writer for the titular newspaper, writing on articles such as Five and Three not catching balls. They are yet to make a reappearance.
Operators were introduced in "The Number Playground Chronicle!". They are based upon mathematical operators. Currently not much info is known about them. They have not made another appearance since.
Fractions were introduced in "The Number Playground Chronicle!". Not much is known about them so far, but they appear exclusively in the aforementioned comic.
Polyhedrons were introduced in "The Number Playground Chronicle!". Currently not much info is known about them, as they do not appear anywhere else.
Trivia
The term "Algebralian" (also spelled "Algebralien") was invented by fans of Battle for BFB, and was later adopted for use by Cary Huang, solidifying the nickname as an official name.
Blocky • 
Bubble • 
Coiny • 
Eraser • 
Firey • 
Flower • 
Golf Ball • 
Ice Cube • 
Leafy • 
Match • 
Needle • 
Pen • 
Pencil • 
Pin • 
Rocky • 
Snowball • 
Spongy • 
Teardrop • 
Tennis Ball • 
Woody • 
Bomby • 
Book • 
Donut • 
Fries • 
Gelatin • 
Nickel • 
Puffball • 
Ruby • 
Evil Leafy • 
8-Ball • 
Balloony • 
Barf Bag • 
Basketball • 
Bell • 
Bottle • 
Bracelety • 
Cake • 
Clock • 
Cloudy • 
Eggy • 
Fanny • 
Firey Jr. • 
Foldy • 
Gaty • 
Grassy • 
Lightning • 
Liy • 
Lollipop • 
Loser • 
Marker • 
Naily • 
Pie • 
Pillow • 
Remote • 
Saw • 
Stapy • 
Taco • 
Tree • 
TV • 
Profily • 
Price Tag • 
Winner
David • 
Dora
Yellow Face
Robot Flower • 
Roboty
Four • 
X • 
Two
Black Hole • 
Nonexisty
