If the independent variable x is infinitely close to x0 (or |x| increases infinitely) and the function value |f(x)| increases infinitely, it is said that f(x) is infinite when x→x0 (or x→∞). For example, when x→ 1, f (x) =1(x-1) 2 is infinite, and when n→∞, f (n) = n2infinity. The reciprocal of infinity is infinitesimal. It should be noted that no matter how big the constant is, it is not infinite.

It can be proved that the power set of any set (the set formed by all subsets) is greater than the original set. If the original cardinality is a, then the cardinality of the power set is recorded as? (2 to the a power). This is the so-called Cantor theorem. For two infinite sets, whether the bijection between them can be established can be used as a criterion to compare their sizes.

Unable to think

From the mathematical point of view, modern quantum field theory has very beautiful gauge symmetry, and its renormalization has also won the Nobel Prize in physics, so we are convinced of the correctness of modern quantum field theory based on QED. Because this mathematical beauty and renormalization have not solved the most basic problems that modern quantum field theory needs to solve, such as how particle spins are produced, what factors determine mass and so on. It cannot be used as the basis of belief theory.