Cantor's diagonal argument but for dimensional reduction
As I understand you can also apply Cantor's diagonal argument to a matrix (or well just write columns below eachother), thus proofing that you can always reduce an n-dimensional tensor to a 1 dimensional vector. Similarly, you can reduce an n-dimensional vectorspace to 1 dimension. For example, you could encode all the (natural) numbers in an n-dimensional vector in only one ("1D") number following Gödel, like this: 2^n_1*3^n2*...*p^n_i