Internal and External Sets

Abstract

In the construction of *ℝ as an ultrapower in Chapter 3, each sequence of points r = 〈r _n : n ∈ ℕ〉 in ℝ. gives rise to the single point [r] of *ℝ., which we also denote by the more informative symbol [r _n ]. Equality of *ℝ-points is given by

$$ \left[ {r_n } \right] = \left[ {s_n } \right]\,iff\,\left\{ {n \in \mathbb{N}:r_n = s_n } \right\} \in F $$

.