1. Otherwise, Weierstrass was very impressed with Riemann, especially with his theory of abelian functions.

2. The numbers π and e are not algebraic numbers (see the Lindemann–Weierstrass theorem); hence they are transcendental.

3. The epsilon-delta version of Weierstrass and Cauchy developed a rigorous formulation of the logic and calculus involved.

4. Compactness Characterization Theorem Suppose that K is a subset of a metric space X, then the following are equivalent: K is compact, K satisfies the Bolzanno-Weierstrass property (i.e., each infinite subset of K has a limit point in K), ; K is sequentially compact (i.e., each sequence from K has a subsequence that converges in K).