The only place I see a space (aside from within tables) inserted with some regularity is surrounding an equals sign to more clearly separate a right-hand from left-hand side of an equation. Aside from that, I have encountered similar places where it has been both inserted and left out, particularly within some containerized object of at least somewhat distinct constituents ⟨[{(a, b, c, ...)}]⟩, but more commonly without. Besides maintaining consistency within single handling, is there a standard correct usage (and non-usage) of a using a space in mathematical statements?
Logically I would think that a space should be used between more distinct parts, such as solutions within a set as contrasted to coordinates assigned to a solution. One place where absence of a space could hinder clarity is with an especially long number, particularly one with an absval greater than or equal to 10^6 that in normal entry often has comma[,]s (sometimes space[ ]s or period[.]s) for readability. Are there any places where spacing is used without a comma? Ever intentional different lengths of spacing (outside of hand-written text)?
The best comment above may have been the one about whatever makes it easier to read. Using Euclid's formula as an example, which of these to you find easier? $$\text{Euclid's formula is } A=m^2-n^2, B=2mn, C=m^2+n^2\text{ with commas}.$$ $$\text{Euclid's formula is }\quad A=m^2-n^2\quad B=2mn\quad C=m^2+n^2\quad\text{ with "\quad"s}.$$ Another case is the right ceiling function after a radical $$\lceil\sqrt{X}\rceil\quad \text{vs}\quad \lceil\sqrt{X}\space\rceil\quad \text{the latter with "\space" in front of }"\rceil"$$ There must be a hundred places where "space" decisions need to be made.
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