简化了条件表达式

Signed-off-by: szdytom <szdytom@qq.com>
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方而静 2025-07-28 22:40:33 +08:00
parent 3d5b9d595a
commit 3e2891e1af
Signed by: szTom
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@ -63,19 +63,19 @@
$infinity$ $-infinity$ 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 $RR union {infinity, -infinity}$ $RR$ 上的向量空间吗?解释一下。