Question 457927
Take note that *[tex a + b - ab = -(a-1)(b-1)+1] (a factoring technique I've heard as "Simon's Favorite Factoring Trick" on a math website but I don't know if it really has a name). The numbers a-1 and b-1 range between -1 and 0, so


*[tex \LARGE 0 < (a-1)(b-1) < 1]


*[tex \LARGE -1 < -(a-1)(b-1) < 0] Add 1 to both sides:


*[tex \LARGE 0 < -(a-1)(b-1) + 1 < 1]


*[tex \LARGE 0 < a + b - ab < 1] and we are done.