I see. I always had the impression that ~せず, is just ~せずに with the particle に omitted, but this is not the case, right?
I have one more thing about ~しないで that I would like to ask. ~しないで can be used to express "cause/reason" too, right? For example:
住所も電話番号も分からないで、連絡が出来なかった。
And just to make sure...分からなくて, 分からず and 分からずに are correct too?