$|a – b| < ε, \forall ε > 0 \iff a = b$ resurfaces on standardized tests to 17 year old (y.o.) students, who can memorize and regurgitate [the proof](https://math.stackexchange.com/a/1249401) to earn full marks. But the [glut](https://math.stackexchange.com/q/1426290) of [duplicates](https://math.stackexchange.com/q/2312613) substantiates that most students can’t intuit it! How can I demystify this equivalence, to 17 year olds? It's counterintuitive and paradoxical for $<$ and $=$ to become equivalent! 

How does the $<$ uncannily transmute to an $=$? 

Vice versa, how can $=$ eerily transmogrify into $<$?