Question 482770
I'll write the numbers given as fractions:
{{{ .142 = 142/1000 }}}
{{{ .143 = 143/1000 }}}
------------------
Multiply both sides by {{{10}}}
{{{ .142 = 1420/10000 }}}
{{{ .143 = 1430/10000 }}}
------------------
If I add {{{ .0003 }}} to top and bottom
of {{{ 1420 / 10000 }}}
{{{ 1423 / 10003 = .1422573 }}}. . . 
is less than {{{ .143 }}}, and, since both
{{{ 1423 }}} and {{{ 10003 }}} are prime,
the result is irrational