As we all know, all expressions in standard Boolean logic can be represented using only a finite number of different connectives. In fact, each expression is equivalent to an expression that only uses NANDs. Although standard logic has many applications in computer science, time-dependent logics seem to be needed to describe and express facts about concurrent processes. This paper cites previous results that show that if time can be a general ordered structure, then no finite number of connectives can suffice to represent all expressions, while if time is linearly ordered then a finite number of connectives do suffice. The paper shows that if time is an infinite discrete tree with an unbounded branching factor, then no finite number of connectives suffice. The proof depends on the fact that certain formulas in n variables are not equivalent to any expression with fewer variables and that this property can be maintained as one builds an infinite branching structure. The author conjectures that if the branching factor is bounded then a finite number of connectives suffice. For such an abstruse topic, this paper is rather easy to follow because the author has included explanations after many of the theorems and definitions.