‼️INFORMATIVE POST FOR ALGEBRALIEN SIDE OF THE OSC‼️
Hello OSC Tumblr ! I have noticed that a lot of people in the OSC in general don't know as much about mathematics, due to the much younger age demographic I'd guess? And that's sort of led to people misidentifying algebraliens and accidentally spreading misinformation about how they work. Anyway I thought I'd try and help people out by sharing some of the stuff I've learnt from my maths studies (and my autism), so people can more accurately make fan content I guess I dunno I'm just bored. Yay!
Basically, each category contains just what the term means in real mathematics, plus how it's typically used within portrayals of algebraliens, and any common misconceptions I've noticed.
Note that if anyone wants me to explain any more complicated mathematical concepts I'm available! I love to teach people about things! I can even add them onto this post if people want :)
Click the read more to see the informative part !!!
INTEGERS
Integers are fairly easy to understand so I don't see people confused here often, but I figured I'd add a section here anyway.
Integers are whole numbers, so no decimals or fractions! Integers can be negative too ! They can't be imaginary though (imaginary numbers involve surds, which is like square root 2, as an example. She's a surd! Not all surds are irrational though.) Surds also are not integers. This is also consistent with portrayals in BFDI.
VARIABLES
Variables are very commonly misunderstood in the OSC, usually by people who haven't advanced as much in maths yet. Variables are a way of representing a mathematical value that changes!
For instance, lets say you wanted to keep track of how many apples you have on a piece of paper. You start with 3, so you write down 3! Then, you eat an apple. Since you now have two apples, the 3 doesn't work anymore! So, you cross it out and write down a 2 instead. But, if the number of apples keeps changing, eventually you'll run out of paper. That's what variables are for!
If you use 'x' to represent how many apples you have, and write it down, x is then equal to whatever number of apples you have at the time. So, if you have 3 apples, the x represents 3! If you eat an apple, x now represents 2!
The same principle applies to algebraliens in BFDI. Variables are known to not keep the same value forever, it changes! (Stated in the plush announcement video, and never disproven in canon). In mathematics, if the value represented by a variable did not change, you would call it a 'constant' instead.
Variables are commonly represented using the arabic (a,b,c, etc) alphabet or the greek (alpha, beta, gamma, etc) alphabet, but some variables are represented by other things too. In mathematics, variables are just a way of representing a changing value, so they can technically look like anything! However, in BFDI specifically, variables (including recommended characters!) are consistently Only visually represented with letters. Of course, you can ignore that if you'd like, but I figured I'd make it known anyway.
One final misconception I've seen people have is specific to X Variable. It seems to be a common misconception that X variable and the multiplication symbol are the same thing, given that in early BFB, the contestants mistakenly think that they multiplied 4 by 0 using X and Donut. However, this was revealed in a future episode to be false, as X had ran away during the incident before 4 and Donut had fused.
Granted it's never specifically stated that X can't do this, but as the creators are both quite interested in mathematics and science, it would make no sense to do this sort of thing. In short, X Variable cannot multiply things together, and variables in general cannot do anything other than represent a value (mathematically speaking), as that is what the word 'variable' means.
IRRATIONALS
Irrational numbers are numbers which cannot be represented as a fraction made of rational (non-irrational) numbers. All integers, fractions, etc can be represented with these fractions, by virtue of fractions like 2/1 being equal to 2.
So, irrational numbers contain any surds (numbers involving the root symbol) and any numbers like pi, tau, or euler's number.
fun fact: the more commonly used name for euler's constant is actually euler's number!
I will be honest I haven't actually seen any misconceptions with irrationals as people don't seem to have irrational OCs often. Regardless I figured it would be best to include!
OPERATORS
Operators aren't a canon class of algebralien in BFDI, but I figured I'd include them anyway as an explanation of what makes them not a part of the above classes.
Operators, in mathematics, are any non-number symbols (including variables under the definition of number). Basically, there's the basic levels of operators, such as +-×÷=, but there's also more complicated operators when you move up to Calculus, such as the integral symbol! (Derivatives are a weird category of sort of variable but sort of operator, so I'd probably put them in their own category for ease of use. They do mainly function as operators, but can interact with each other in very number-like ways in mathematics).
In BFDI, the only examples of operators we've seen are rocks on the ground of the algebra planet in the Subcount Specials, or the orange ones in XFOHV. The most prominent rock operator is the division symbol, but the addition symbol is shown in the 1.5 million subscriber special too. Don't let that stop you from making operator OCs though! Have fun regardless!!
What seperates operators from the above categories is that operators are ways of linking several numbers together, or representing a way you should change that number, as opposed to being numbers themselves.
OTHER CATEGORIES
There are many mathematical concepts that algebraliens in BFDI have yet to represent. For example, the integration and differentiation (derivative) symbols have yet to be used even in fan-content from what I have seen! Additionally, no one ever seems to use the greek alphabet for their variables. I've also never seen any trigonometric functions, or graphs, or summations, etc etc.
If you want to make a more unique looking algebralien OC, I would recommend researching more advanced mathematical concepts! I think it would be cool to see more varied algebraliens around.
AFTERWORD
Please don't take my words as a rule or anything!! Creating stuff should be fun and I get that. But if anyone is struggling to understand how these algebralien classes work and what they mean, ask me! I'm always happy to teach people about things :)
- W Variable
Byee !!
Note: I wanted to add more images but the app won't let me v_v such is life when you decide to do these things on a whim
Second note: the reason any self-referential words are coloured pink is so people know whether it's Me (W) or Two alter talking. If you see green, that text is referring to them! (They didn't want to talk on this post though really)
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You've heard of integer primes, but have you heard of different kind of primes? One of the most beautiful pictures in mathematics I've recently seen is this:
This is a picture displaying the Eisenstein primes and the rest of the post will be me explaining where this comes from.
Firstly, to understand what Eisenstein primes are, we need to know what Eisenstein integers are! An Eisenstein integer is a complex number of the form z = a + b w where a,b are integers and w = e^(2/3 pi i). Normally a small letter omega is used instead of w. Notice that w is a third root of unity, i.e. w³ = 1.
Appending this complex w to the regular integers has some consequences. In particular, we can now view the eligible numbers on the complex plane to get this picture:
The Eisenstein integers correspond exactly to places where two dotted lines cross. As such, where normally one can view integers as laying on a 1-d line, we can now view Eisenstein integers as laying on a 2-d lattice!
Now one may start to wonder if, just like in the integers, one can have Eisenstein integers which are not divisible by other Eisenstein integers. In more mathematics: We call a number p an Eisenstein prime if p cannot be written as a*b where a,b are Eisenstein numbers which are not +-1, +-w, +-w² (the units in this system).
It turns out that some regular primes are still primes in the Eisenstein integers. For example, 2 can still not be decomposed. However, 3 can! We may write 3 = -(1+2w)(1+2w) which means that 3 is not an Eisenstein prime. One may investigate this further (using abstract algebra) to arrive at the picture at the top of this post. The 6-fold rotational symmetry is due to the Eisenstein integers having 6 units.
Of course a natural question is why take a third root of unity and not an nth root? This is a very interesting question and leads to the study of (integer rings of) cyclotomic fields! This concludes fun math fact tuesday
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tfw someone asks how you did math in your head so quickly, but you don't really feel like getting into the social dynamics of your lifelong arabic numeral OCs
