According to Heine's theorem, finding function limit can be transformed into finding sequence limit, and finding sequence limit can also be transformed into finding function limit. Therefore, all the properties of function limit can be proved by the related properties of sequence limit. Heine theorem shows the relationship between function limit and sequence limit.

According to the necessary and sufficient conditions of Heine theorem, we can also judge whether the function limit exists. Therefore, Heine theorem plays an important role in finding the limit of sequence or function. Heine theorem was given by German mathematician Heine. By applying Heine theorem, people can turn the function limit problem into a sequence problem, so people also call it the resolution principle.

Presenter:

German mathematician. Born in Berlin, died in Harley. Independent discovery of Heine theorem.

1. Expounds the concept of uniform convergence and proves the uniform convergence theorem of continuous functions.

2. We independently discovered and used Heine theorem (1895, Borel proved the finite covering theorem, which is the famous Borel covering theorem. Because Heinrich Eduard Heine also used this property in his proof of uniform continuity, this theorem is also called Heine-borell theorem, which bridges the limit of sequence and the limit of function.

3. The arithmetic definition of irrational number is given.

Other achievements: ball function, Lame function, Bessel function, etc.