let X, A be set ; ( chi (A,X) is without+infty & chi (A,X) is without-infty )
rng (chi (A,X)) c= {0,1}
by FUNCT_3:39;
then
( not +infty in rng (chi (A,X)) & not -infty in rng (chi (A,X)) )
;
hence
( chi (A,X) is without+infty & chi (A,X) is without-infty )
by MESFUNC5:def 3, MESFUNC5:def 4; verum