C. K. Raju
Indian Institute of Advanced Study
Rashtrapati Nivas, Shimla
Indian NCERT class XI text says:
First, we give an intuitive idea of derivative (without actually defining it). Then we give a naive definition of limit and study some algebra of limits3
What the student typically learns about set theory is something as follows.
"A set is a collection of objects"
"A set is a well-defined collection of objects"