Brain dump

I # In an intertial frame of reference (i.e. a frame of reference undergoing zero acceleration), an object at rest … ...

Newtonian Spacetime differs from Relativistic spacetime in that time is considered an absolute (i.e. \(t^{\prime} = … ...

The set of points surrounding a point \(p\) in a set \(V\), such that \(p \in \mathbb{R}^{n}\), within a radius …

A set and a function which defines the distance between two points on that set An ordered pair \((X, d)\), where \(X\) … ...

Locality refers to: A property \(P\), of a point \(x\), which holds true near every point around \(x\). As an example: …

Isotropy means that direction is not preferred, and that there is uniformity in any orientation. Specifically, in …

A function is injective (“one-to-one”) if \(x \neq x^{\prime} \Longrightarrow f(x) \neq f(x^{\prime})\) …

Above are two frames in Cartesian coordinates, \(S\) and \(S^{\prime}\). We have coordinates \((x, y, z)\), which define … ...

Homogeneous means that location is not preferred, that the physics are the same at any point. Specifically, in …