In the coordinate plane xOy, depict the set of all points such that ∣y−[x]∣=2−y−[x], where [x] is the integer part of x, i.e. the largest integer not exceeding x.
Solution
Вихідне співвідношення рівносильне системі ⎩⎨⎧y=1,[x]=1;y≤2−[x]. Слід зобразити множину точок {(x;y):1≤x<2,y<1}∪{(x;1):x<2}.
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.
Source: MathNet,
licensed CC-BY-4.0.
Statement and solution reproduced as published; topic and difficulty added by this site.