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I have a curiousity.

Is there a theorem or conjecture like this ?

"For any irrational number, like square root of 2, we can always find the approximation of at most 3 rational numbers with just +,-,* and /" ?



Continued fractions can be used to find best rational approximations. But you can also just use floor(x*10^n)/10^n.


If you're allowing division, you can get arbitrarily close with just two (potentially very large) integers.


I guess the more interesting conjecture would be stating something about the size of the integers compared to the irrational number




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