One Place Function?

Still from the same document we saw on the other post comes this one:

So, as said before, i should be a reserved letter in Mathematics, so that it shouldn't mean increment, not really. Maybe that is what they have done here, but they shouldn't have done that, that is all. You don't take the symbol for the set of the real numbers, which is the R with double strike, and insert it somewhere to mean variable, you simply don't. The name gives you no clue as to the nature of the thing named, he says, that making the criticism. Yet, in Mathematics, we should try to give clues also through the names we give to things. 

One-place function is not a good name. Perhaps they meant a real function. If so, they should just have said that: A real function or an R^2 function or a Cartesian function. A two-place function could then be an R^3 function (you have two coordinates in the domain, so that you use those to get your result, and that would then form the third coordinate), we suppose. 

The occurrence of the variable is free is a dodge claim, given the context. We imagine he refers to Logic and no quantifiers are noticed. We never saw a variable that is the name of a number. We suppose he meant the variable, in this case, is not a place holder for a number. If not, then we don't know what a variable is anymore, we suppose. Now, what function? If there is no equal sign, we don't really have a function there. Again, x and x+i are not points: They are at most coordinates or elements of the domain. 

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