$|a – b| < ε, \forall ε > 0 \iff a = b$ resurfaces on standardized tests to 17 year old (y.o.) students, who can memorize and regurgitate the proof to earn full marks. But the glut of duplicates 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 $<$?