2
votes
1answer
191 views

How many flavors should a notational system offer for rank-1 tensors?

The notation for tensors is like the plumbing in a very old Vermont farmhouse. It may once have been intentionally designed, but after that it just evolved. As an example, it seems that depending on ...
10
votes
5answers
4k views

If d/dx is an operator, on what does it operate?

If $\frac{d}{dx}$ is a differential operator, what are its inputs? If the answer is "(differentiable) functions" (i.e., variable-agnostic sets of ordered pairs), we have difficulty distinguishing ...
2
votes
2answers
2k views

Is the notation $f(x)$ “deprecated by professional mathematicians” (as claimed by Wolfram)? [closed]

Wolfram's MathWorld website, at the page on functions, makes the following claim about the notation $f(x)$ for a function: While this notation is deprecated by professional mathematicians, it is ...
14
votes
6answers
4k views

What's the notation for a function restricted to a subset of the codomain?

Suppose I have a function f : A → B between two sets A and B. (The same question applies to group homomorphisms, continuous maps between topological spaces, etc. But for simpicity let's restrict ...
4
votes
2answers
1k views

Why are the Dynkin diagrams E6, E7 and E8 always drawn the way they are drawn?

The Dynkin diagrams of type ADE are ubiquitous in mathematics as solutions of various classification problems. The diagram E6 is usually drawn by five dots in a row with a sixth dot above the third, ...