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Fixed the question formation - missing auxiliary (or helping) verb - see e.g. <https://www.youtube.com/watch?v=t4yWEt0OSpg&t=1m49s> (see also <https://www.youtube.com/watch?v=kS5NfSzXfrI> (QUASM)) - alternatively, drop the question mark.
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edit approved Oct 19, 2023 at 4:41
Peter Mortensen
edit approved Oct 19, 2023 at 4:41
Peter Mortensen
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To 17 year olds, how tocan I explain that 2two numbers with arbitrarily small difference are equal?

$|a – b| < ε, \forall ε > 0 \iff a = b$ 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 y.o.? It's counterintuitive and paradoxical for $<$ and $=$ to become equivalent!

How does the $<$ uncannily transmute to an $=$?
Vice versa, how can $=$ eerily transmogrify into $<$?

To 17 year olds, how to explain that 2 numbers with arbitrarily small difference are equal?

$|a – b| < ε, \forall ε > 0 \iff a = b$ 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 y.o.? It's counterintuitive and paradoxical for $<$ and $=$ to become equivalent!

How does the $<$ uncannily transmute to an $=$?
Vice versa, how can $=$ eerily transmogrify into $<$?

To 17 year olds, how can I explain that two numbers with arbitrarily small difference are equal?

$|a – b| < ε, \forall ε > 0 \iff a = b$ 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 y.o.? It's counterintuitive and paradoxical for $<$ and $=$ to become equivalent!

How does the $<$ uncannily transmute to an $=$?
Vice versa, how can $=$ eerily transmogrify into $<$?

deleted 4 characters in body; edited title
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user95017
user95017
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How to explain to To 17 year olds, how to explain that two2 numbers whose difference iswith arbitrarily small difference are equal?

$|a – b| < ε, \forall ε > 0 \iff a = b$ 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 oldsy.o.? It's counterintuitive and paradoxical for $<$ and $=$ to become equivalent!

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

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

How to explain to 17 year olds that two numbers whose difference is arbitrarily small are equal?

$|a – b| < ε, \forall ε > 0 \iff a = b$ 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 $<$?

To 17 year olds, how to explain that 2 numbers with arbitrarily small difference are equal?

$|a – b| < ε, \forall ε > 0 \iff a = b$ 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 y.o.? It's counterintuitive and paradoxical for $<$ and $=$ to become equivalent!

How does the $<$ uncannily transmute to an $=$?
Vice versa, how can $=$ eerily transmogrify into $<$?

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edit approved Oct 17, 2023 at 14:47
user3840170
edit approved Oct 17, 2023 at 14:47
user3840170
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How to explain to 17 year olds why = can become equivalent into an <, and vice versathat two numbers whose difference is arbitrarily small are equal?

$|a – b| \color{red}{<} ε, \forall ε > 0 \iff a \color{limegreen}{=} b$$|a – b| < ε, \forall ε > 0 \iff a = b$ resurfaces on standardized tests to 17 year old (y.o.) students, who can memorize and regurgitate the proof to earn full marks. But the glut of duplicates substantiates that most students can’t intuit it! How can I demystify this equivalence, to 17 year olds? It's counterintuitive and paradoxical for $\color{red}{<}$$<$ and $\color{limegreen}{=}$$=$ to become equivalent!

How does the $\color{red}{<}$$<$ uncannily transmute to an $\color{limegreen}{=}$$=$?

Vice versa, how can $\color{limegreen}{=}$$=$ eerily transmogrify into $\color{red}{<}$$<$?

How to explain to 17 year olds why = can become equivalent into an <, and vice versa?

$|a – b| \color{red}{<} ε, \forall ε > 0 \iff a \color{limegreen}{=} b$ 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 $\color{red}{<}$ and $\color{limegreen}{=}$ to become equivalent!

How does the $\color{red}{<}$ uncannily transmute to an $\color{limegreen}{=}$?

Vice versa, how can $\color{limegreen}{=}$ eerily transmogrify into $\color{red}{<}$?

How to explain to 17 year olds that two numbers whose difference is arbitrarily small are equal?

$|a – b| < ε, \forall ε > 0 \iff a = b$ 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 $<$?

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user95017
user95017
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