This will just be a very short post about a minor conundrum I noticed. Suppose we are working over the real numbers . The term represents a two variable function. However, when you simplify it to get the term , it now represents a one variable function. This is a bit puzzling for me. I guess, then, that you have to keep track of the arity of the function represented by a term when you simplify it.
Comments
a multivariable function can always be constant with respect to any of its variables. the number of vartiables is determined by the domain and not the formula