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Lebl-Basic-Analysis-I
· Problem 1.2.14
Real Numbers
Mathematics · supremum-infimum-algebra
Problem
Prove
sup
{
x
∈
Q
:
x
2
<
2
}
=
sup
{
x
∈
R
:
x
2
<
2
}
\sup\{x \in \mathbb{Q} : x^2 < 2\} = \sup\{x \in \mathbb{R} : x^2 < 2\}
sup
{
x
∈
Q
:
x
2
<
2
}
=
sup
{
x
∈
R
:
x
2
<
2
}
.
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