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Actually integers are very poorly approximable by rational numbers, even though each integer is very well approximated by a single specific rational number The
by henrydark 4y ago
Actually integers are very poorly approximable by rational numbers, even though each integer is very well approximated by a single specific rational number
The definition of "well approximated" is that there are infinitely many good approximations, not just one really good one, and this is what integers, and algebraic numbers in general, fail to have
- SilasX 4y agoEvery integer has an infinite number of combinations of integers that add up to it.
- henrydark 4y agoIndeed! Mathematics is a lot about defining something and then proving stuff (and sometimes going the other way around). Different combinations giving the same approximation are considered a single approximation, namely the result of the combination