• ## crimboi[21] 模仿大赛

Rotman algebraic topology上的题, 个人认为出的非常好, 极大增进了读者对\pi_1(S^1)计算过程的理解. 题面 A group G which is also a topology space is called a topological group if \mu:G\times G\to G:(x,y)\mapsto xy and i:G\to G:x\mapsto x^{-1} are contin……
HDD 10小时前
• ## Building a Clear Programming Language for Newcomers

This is a joke Introduction Many new programmers are often confused about a very important concept in programming: the variable lifespan. For example, one could not understand why the variable "a" is "not defined" when it's clearly there: int x=3; ……
XGN 1天前
• ## Orange Boy Can You Solve It Out? Ep. 61

思考题 featuring Hikari again! Guess the string Hikari and her master Ninetail are playing a game. Hikari thinks of a string S with lower-case letters, and Ninetail asks her to make q modifications one by one. Each modification can only be one of t……
XGN 2024年9月4日
• ## crimboi[20] 泛函分析心犯寒

Dieudonne的题, 真实难度不好说, 回顾一下发现其实挺简单的. 题面 Let E be a Hilbert space, F a dense linear subspace of E, distinct from E. (For example E space of l^2 sum of a suitable countable linear independent set and F space of finite sum of thi……
HDD 2024年8月1日
• ## 小科普之Principal Ideal Domain is not necessarily Euclidean Domain

It's a well known fact that Euclidean domains are principal ideal domain by taking the element in a certain ideal with smallest \varphi value. Yet the converse is false, and one counterexample just lies among our familiar algebraic integer rings, \……
HDD 2024年7月10日
• ## crimboi[19] 吃屎绕大弯

题目背景 为证一个非零吃大师 题面 Assuming AC, prove that for a integral domain R, if any nonzero prime ideal P contains a nonzero prime (p), R is UFD. 先想再看提示哦 提示 Let S be the set of elements that are prime factori……
HDD 2024年7月6日
• ## 微科普之Necessary and sufficient condition for a sequence to be graphic

This proof is due to Choudum. A sequence of nonnegative integers (d_1,...,d_n) is called graphic if there is a simple graph G with V(G)=\lbrace v_1,...,v_n\rbrace and d(v_i)=d_i. It's very easy to show that if a nonincreasing sequence, i.e. d_1\ge ……
HDD 2024年6月29日
• ## [indiscipline][2] 初中不等式

飞机上半昏迷状态下以为无法调整, 暴力算出来的搞笑解答. 非常具有统计色彩 (nod) 题面 A simple graph G is called complete k-partite if there's a partion of V(G): A_1,..., A_k s.t. for all i there's no edge with both vertices in A_i , and for any v\in A……
HDD 2024年6月28日
• ## 2024春南京大学信计强基离散数学期末考试题目速报(Prof. Yuan Zhang, Penghui Yao)

2小时，100分满分，内容是图论，开卷，可带电子设备，可查阅课程笔记和资料，不可上网。点击长图查看：
XGN 2024年6月14日
• ## 中科普之alternating group is simple for n>=5

It's a well-known fact that the alternating groups, A_n, are simple for n\neq 4, with small cases like A_1, A_2, A_3 very easy to verify. Yet most proofs of n\geq 5, including Hungerford's, relies heavily on 'magical' permutation composition, which……
HDD 2024年6月5日