Zeroth homotopy group of the sphere spectrum

Example 4.4.25. By Remark 2.4.20, there is an isomorphism \(\deg \colon \pi _n(S^n) \xrightarrow {\cong } \Z \) for every \(n\geq 1\), and the suspension maps correspond to the identity of \(\Z \). It follows that there is an isomorphism \(\pi _0(\S ) \cong \colim _n \pi _n(S^n) \cong \Z \).