kogasa

No, that's what induction is. You prove the base case (e.g. n=1) and then prove that the (n+1) case follows from the (n) case. You may then conclude the result holds for all n, since we proved it holds for 1, which means it holds for 2, which means it holds for 3, and so on.

It's not actually claiming that all horses are the same color, it's an example of a flawed induction argument

For an alternative that doesn't sound insane, try turkey a la king. Turkey in a creamy sauce on puff pastry or toast.

They're already doing this or may as well be

Empty set is ∅, slashed zero is 0︀ (if your browser decides to render the unicode variant) or 0︀ in html

Learn the difference, it could save your life!

(It could not actually save your life)

"qrstuv" isn't an abbreviation. It's the alphabet dawg

She didn't step on it, she apparently used her thumb and damaged one of the buns in the pack

Not really, you need to have a basic understanding at least

You might be thinking of a [connection of an affine bundle](https://en.wikipedia.org/wiki/Connection_(affine_bundle). You could learn it through classes (math grad programs usually have a sequence including general topology, differential topology/smooth manifolds, and differential geometry) or just read some books to get the parts you need to know.

Manifolds and differential forms are foundational concepts of differential topology, and connections are a foundational concept of differential geometry. They are mathematical building blocks used in modern physics, essentially enabling the transfer of multivariable calculus to arbitrary curved surfaces (without relying on an explicit embedding into Euclidean space). I think the joke is that physics students don't typically learn the details of these building blocks, rather just the relevant results, and get confused when they're emphasized.

For a tl;dr about the concepts mentioned:

• A manifold is a curve, surface, or higher-dimensional object which locally resembles Euclidean space around each point (e.g. the surface of a sphere is a 2D manifold; tiny person standing on a big sphere perceives the area around them to resemble a flat 2D plane).

• Differential forms are "things that can be integrated over a manifold of the corresponding dimension." In ordinary calculus of 1 variable, that's a suitably regular function (e.g. a continuous function), and we view such a function f(x) as a differential form by writing it as "f(x) dx."

• A connection is a way of translating local tangent vectors from one point on a manifold to another in a parallel manner, i.e. literally connecting the local geometries of different points on the manifold. The existence of a connection on a manifold enables one to reason consistently about geometric concepts on the whole manifold.

The actual problem was to determine the shape of the largest sofa that could fit around a given corner. The shape had been known for some time as the largest known shape, but only recently was it proved optimal.

No, they're not sure. You're correct.