scitposting 1: calculus is the archenemy of discrete math

I mean, calculus deals with s m o o t h stuff, like the real numbers, which is infinite and uncountable. And continuous functions are s m o o t h and unbreaking, an unbreaking line or chain of points that are not isolated. They’re chads, these points are chads, with a dense number of points always surrounding them. And differentiable functions are even s m o o t h e r, because they’re continuous functions that are always cURVing.

OK WELL what about discrete math? Discrete math loves being isolated. Discrete maths isolates itself from other points (and people). Discrete maths loves to be counted, unlike the cooler real numbers that can’t be counted. Also a lot of it involves too much proof by induction, proof by contradiction, etc. etc.

Calculus, on the other hand, is a colorful girl. What other stuff does calculus like? Lol, they even capture higher dimensional shapes and regions, and even arbitrary regions. Connected arbitrary regions are also involved in calculus. You need the area of a general 2D shape? Use double integrals!! You need the volume of a general 3D region? Use triple integrals!!

Does discrete math even have these s m o o t h regions and shapes? No, it doesn’t. The closest thing it even has to shapes are graphs that represent the vertices or edges of polygons and polyhedra and higher polytopes. Well, the area and volume of these polytopes can be found using calculus… but then again there are also interesting topological concepts found in examining the vertices and edges of these shapes.

But calculus even involves Euclidean vectors in its gang, and Euclidean vectors always have direction in life. And if we have a continuous vector-valued function, it means that there is a continuum of vectors in a vector field, all flowing towards a direction. That direction is given by calculus. What a madman.

I can go on, lol. The ideas of calculus carried over to differential equations, ordinary and partial. Any function described by a differential equation is s m o o t h, like, really s m o o t h over a certain region. The myth the legend calculus introduced the idea of derivatives, and relating the function’s derivatives in a single equation like y” + t²y’ – y = sin(t) or u_xx + u_yy + u_zz = a²u_tt might seem to give us more problems, but calculus knows that tackling these problems has its uses. It makes the boi physics stronger, it makes us stronger.

But then again… discrete maths makes computer science stronger. Like the graphs I mentioned are used in computational geometry and network theory.

But discrete maths loves to be counted and I don’t like counting. I like measuring.

Ok but also remember more people love discrete maths more than calculus and differential equations because of all the interesting puzzle-derived problems discrete maths has. I think people like solving puzzles, Rubik’s cube, Hanoi towers, zero sum games…

Ok fine that’s your opinion hmmmp.

ADDENDUM: Whatever, I like limits more than induction, which is why I like continuous mathematics more than discrete mathematics. Also I’m a physics major, not a computer science major. And I was never fond of puzzles so maybe that’s why I love continuous mathematics more.