I am using Spivak calculus. The reason why epsilon-delta definition works is for every ε>0, we can find some δ>0 for which definition of limit holds. Spivak asserts yhat if we can find a δ>0 for every ε>0, then we can find some δ1 if ε equals ε/2. How is this statement possible? Since ε>0, then (ε/2) must be greater than zero. So, naturally one would argue that, if we can find δ for an ε>0, we can also find δ1 for (ε/2)>0. But a question arises for me. Why can't we say that if ε=(ε/2) and is >0, then ε>0. or why cant we say the converse. Why cant the proof start in converse way. Suppose, I can find a δn for every ε= ε^(2) +ε, can we concude the converse that ε must be greater than 0.