diff --git a/sections/1B.typ b/sections/1B.typ index c1d7197..6fe4d15 100644 --- a/sections/1B.typ +++ b/sections/1B.typ @@ -63,19 +63,19 @@ 令 $infinity$ 和 $-infinity$ 是不在 $RR$ 中的不同对象。以最符合直觉的方式定义 $RR union {infinity, -infinity}$ 上的加法和标量乘法。具体而言,两个实数的和和积照常定义,而对于 $t in RR$,我们定义 $ t infinity = cases( - -infinity wide& "若 " t<0 ",", - 0 &"若 " t=0 ",", - infinity &"若 " t>0 ";") + -infinity wide& t < 0, + 0 & t = 0, + infinity & t > 0) wide t (-infinity) = cases( - infinity wide& "若 " t<0 ",", - 0 &"若 " t=0 ",", - -infinity &"若 " t>0 ";") $ + infinity wide& t < 0, + 0 & t = 0, + -infinity & t > 0) $ #tab 以及 - $ t + infinity &= infinity + t = infinity + infinity = infinity "," \ - t + (-infinity) &= (-infinity) + t = (-infinity) + (-infinity) = -infinity "," \ + $ t + infinity &= infinity + t = infinity + infinity = infinity \ + t + (-infinity) &= (-infinity) + t = (-infinity) + (-infinity) = -infinity \ infinity + (-infinity) &= (-infinity) + infinity = 0 $ #tab 具有这样的加法和标量乘法的 $RR union {infinity, -infinity}$ 是 $RR$ 上的向量空间吗?解释一下。