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Bioshock1fullgameupdatedrepack
Download App SuperTime. The Mercenaries 2: European Edition (PC).Q:
Given an irrational number, find the closest rational number with integer part equal to the given irrational number
I am learning different ways of tackling the question.
Given an irrational number $alpha in mathbb{R}$
Find the closest rational number $q$ with integer part equal to $alpha$
I am unable to understand this part of the question: Integer part of $q$ should be equal to $alpha$?
A:
If you know the integer part of a rational number $q$ is $a$ and $alpha$ is irrational, then you can say that $$left|alpha-qright| leq left|alpha-aright|+left|a-qright|=alpha-qcdotfrac{q-a}{q-a}+left|a-qright|= alpha-frac{left(a-qright)left(a+qright)}{aleft(a+qright)}+left|a-qright|=frac{left(a-left|a-qright|right)left(a+left|a-qright|right)}{aleft(a+left|a-qright|right)}+left|a-qright|\=frac{left|a-qright|left(a+left|a-qright|right)}{aleft(a+left|a-qright|right)}+left|a-qright|=frac{left|a-qright|left(a+left|a-qright|right)+left|a-qright|}{aleft(a+left|a-qright|right)}=frac{left|a-qright|left(2a+left|a-qright|right)}{aleft(a+left|a-qright|right)}=frac{left|a-
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