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MathNet 1986 — Part 01 Question 21

Math Olympiad Vault · MathNet 1986 — Part 01

Question 21

We will indicate by $[x],\{x\}$ the integer and decimal parts of the real number $x$. We define a distance between the real numbers $x$ e $y$ $$
d(x, y)=\sqrt{([x]-[y])^{2}+(\{x\}-\{y\})^{2}}
$$ Determine (as junction of intervals) the set of real numbers that are far from the number $3 / 2$ less than $202/100$.