There is no particular reason. For instance, we can hold the function constant in one variable and get two more variants of the function, \$$\chi_m(n) \$$ and \$$\chi_n(m) \$$.

Edit

**Hint:** Hold the variable \$$m\$$ constant at zero, and consider the function \$$\chi_0(n) \$$ . What possible value or values does this function produce on positive values of \$$n\$$? What possible value or values does this function produces on negative values of \$$n\$$?