Can I not let these states of mind exist simultaneously?

f(t)=a(t)+b(t)+c(t)

a(t) approaches zero as t-> infinity.
b(t) approaches zero as t-> infinity.
c(t) approaches one as t-> infinity.

a(t) is bounded: [0, infinity)
b(t) is bounded: (-infinity, 0] 
c(t) is not bounded. 

[1] Just wait it out, man. Just wait it out.
[2] Honestly, whose side are you on? What are you trying to have proven? 
[1] It doesn't accomplish anything (bad science) but that's what I want to watch play out. 
[1] Yes, it is. That's what I want to watch happen. More interesting that way. 
[1] It's good to have that back.