How is it possible to sing when the Lebesgue measure of the rationals is zero?

#1
this year i started studying measure theory, and there was an exercise that really caught my attention... Lebesgue measure basically means 'length of segments of the number line'... like, the lebesgue measure of the interval [0,2] is just 2.

the exercise that caught my attention is to prove that the lebesgue measure of the set of rational numbers amongst the set of real numbers is zero.

in order to harmonise with music, you gotta find a rational multiple of the frequency you wanna harmonise with, or be arbitrary close to one(rational just means numbers which can be written as a fraction)

since our voices are freestyling accross the infinitely dense and uncountable scale of the real numbers, how the fuck do we manage to even harmonise at all? are we ever harmonising, or are we only ever coming close to a note?

since we can cover the rational numbers with a set of measure zero, the rational numbers basically have no size at all. there is mathematical proof of this. in other words, to sing is to locate frequencies that are in a set of measure zero..................... how do people do this at all isn't it beautiful?

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Last edited by laid-to-waste at Dec 11, 2016,
#2
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#3
Because inharmonicity
A poem.
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