The basic problem is thus to know how well irrational numbers can be approximated by rational numbers, to find upper and lower bounds for the "best" rational approximations for a given real number or for a class of real numbers.
The basic problem was to know how well irrational numbers can be approximated by rational numbers, to find upper and lower bounds for the "best" rational approximations for a given real number. Then historically the question springs up how well irrational numbers can be approximated by rational numbers for certain sets of real numbers.