N-sphere is (n-1)-connected

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Statement

Suppose n is a natural number (i.e., n \ge 1). Then, the n-Sphere (?) is (n - 1)-connected. In other words:

By the Hurewicz theorem, this is equivalent (for n \ge 2) to the assertion that S^n is simply connected and the first n - 1 homology groups are trivial.