Definition: Let f be a function. The domain of f is simply its “source” set. Namely, if f is a function from A to B, denoted 
That’s it. There’s really nothing fancy going on here—just names. Just as for codomains, this definition is purely for convenience, but no one would doubt the importance of delivery pizza despite the fact that it’s only there for convenience!
For more on domains, check out lesson 6.
The True Beauty of Math 