Rational numbers

• categories: Real Analysis, Definition

$\mathbb{Q}=\{m/n|m,n\in \mathbb{Z}\}$ with equivalence classes for irreducible form Sum and multiplication are well defined (may be verified that we get the same equivalency class) Order is well defined

Correspondance n/1 → n is isomorphism to N

Not good enough to solve all polynomial equations. Haps sets without LUB.

$\mathbb{Q}$ is ordered field = order is preserved by field operations

Archimidian property

For x, y | x>0 exists n s.t xn > y. Prouved by contradiction