Real Analysis, 131A, Fall 2014 (full set of notes)
... Lemma 1.2.7. For any natural number n, n + 0 = n.
Remark 1.2.8. Note that we cannot apply commutativity of addition, since it does not
immediately follow from the axioms of Definition 1.2.1.
Proof. From Definition 1.2.3, 0 + 0 = 0. So, we induct on n. Suppose n + 0 = n for
a natural number n. We nee ...