You notify her so that you don't stoop to her level. If it were me, I would (and did) say something like "I know I've indicated before that I didn't want to date while we were separated, because I thought we should be trying to work on our marriage instead. But seeing as how you've already obviously moved on anyway, (and seeing as how you can't really work at a marriage when one person has invited a third person into it) I've done some thinking and I have decided that* it would be healthy for me to see what else is out there for me as well. As a courtesy, I wanted to let you know."
*these words were taught to me by Gucci in his posts here, and I really like them. Whenever you use the "I have decided that --" formulation, it shows decisiveness, strength and that you're individuated.
