Every java programmer hates NullPointerException. Indeed, any variable¹ in java can take this special value of null, which indicates a lack of value in this variable. They are like landmines in your code; stomp upon one and boom! Your program is dead. Thus, programming in java is like wading through a minefield. You have to add checks like if (var != null) in a lot of places, which is error-prone and cumbersome².

This series of articles aims to explain why complicated type systems such as λC can be useful in practice, and how such use inevitably leads to the ability to formalize mathematics.

Formalism eliminates falsehood; it does not lead to the truth.

This is the ENS Entrance Exam 1995 Mathematics Written Part. Translated by Tony Beta Lambda.

每一个学习数学的人都或多或少地接触过集合论. 所谓集合论，其研究对象就是集合和它们之间的“属于”关系. 在现代数学的各个分支中，结构性的概念如群、拓扑、\(\sigma\)-代数，其定义的开头总是“设 \(X\) 是一个集合，满足……”更进一步，甚至关系、函数、卡氏积，自然数、有理数、实数等数学的基本概念，也可以在集合论的框架中，只用集合和它们间的“属于”关系严密定义.

This paper studies parity distribution of divisors of all integers up to \(n\), by dealing with a variant of the alternating harmonic series, namely

某次数学分析习题课上，助教提出一个问题：\(\lbrace n \sin n \mid n \in \mathbb N \rbrace\) 是无穷大量吗？