While self studying algebra from Thomas Hungerford I have following question in understanding terminology on page 253 of textbook.
Consider this line of textbook
Let n be a positive integer, K an arbitrary field, E the subfield of symmetric rational functions in $ K(x_{1},..., x_{n} ) $ and $f_1, f_2,..., f_n \in E $ the elementary symmetric functions in $x_1 , x_2,..., x_n$ over K.
What does author mean by $f_1, f_2,..., f_n \in E $?
Does it mean that range of $f_{i}$'s belongs to E?
Clearly, it is a function in variables $x_{1} ,..., x_{n} $.