English: Dedekind cut defining √2, an irrational number, using two sets of positive rational numbers. All those whose square is less than two (red), and those whose square is equal to or greater than two (blue).

...
1/1       = 1
7/5       = 1.4
41/29     = 1.413793103448276...
239/169   = 1.414201183431953...
1393/985  = 1.414213197969543...
√2        = 1.414213562373095...
3363/2378 = 1.41421362489487...
577/408   = 1.41421568627451...
99/70     = 1.414285714285714...
17/12     = 1.416
3/2       = 1.5
2/1       = 2
...

After: File:Dedekind cut sqrt 2.svg.