※ 引述《paperbattle (?)》之铭言：
: 那就来考考各位八卦板友
: (IQ(p) is Intelligence Quotient of a person p)
: There is a p in '9.2' and IQ(p) < ε for all ε > 0.
: For every p and q in '9.2', | IQ(p) - IQ(q) | < ε for all ε > 0.
: Prove that IQ(p) = 0 for all p in 9.2
Prove by contradiction
Assume there exists a p' in 9.2 s.t. IQ(p') > ε' for some ε' > 0.
since p and p' are in 9.2, | IQ(p) - IQ(p') | < ε for all ε > 0,
IQ(p') = IQ(p) < ε for all ε > 0,
which contradicts with the assumption that IQ(p') > ε' for some ε' > 0.
Therefore, the assumption is false,
there does not exist any p in 9.2 s.t. IQ(p) > 0.
中间有些地方感觉好像有点不够严谨 但我自己不是很确定有没有问题
有看出来的话请帮忙指点一下

|IQ(p)-IQ(p')|<ε 要改成 |IQ(p')-0|<εthen | IQ(p') | < ε , for all ε > 0 :)因为 |IQ(p)-IQ(p')|<ε for all ε>0 ,|IQ(p)-IQ(p')|<ε'/2 => IQ(p')-ε'/2<IQ(p)<IQ(p')+ε'/2=> ε'/2<IQ(p) , for some ε'>0 →←

如果没有IQ(p)>=0这个前提，充其量只能证明IQ(p)-IQ(p')=0吧！