for sqrt(2) it is defined as :{x belongs to Q: (X^2) < 2 V X < 0}
for 1 it is defined as : {x belong to Q: X<1}
tO PROVE > you have to prove {x belongs to Q: X<1} IS A SUBSST OF
{X belongs to Q: (x^2) < 2 V X < 0}
for sqrt(2) it is defined as :{x belongs to Q: (X^2) < 2 V X < 0}
for 1 it is defined as : {x belong to Q: X<1}
tO PROVE > you have to prove {x belongs to Q: X<1} IS A SUBSST OF
{X belongs to Q: (x^2) < 2 V X < 0}
And that is straight forward, isn't it? If x is in the Dedekind cut "1" then either x< 0 or . In the first case, x in the Dedekind cut " " because that cut includes "X< 0". In the second case, , what can you say about ?