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简化了条件表达式
Signed-off-by: szdytom <szdytom@qq.com>
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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
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$ t infinity = cases(
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-infinity wide& "若 " t<0 ",",
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0 &"若 " t=0 ",",
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infinity &"若 " t>0 ";")
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-infinity wide& t < 0,
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0 & t = 0,
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infinity & t > 0)
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wide
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t (-infinity) = cases(
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infinity wide& "若 " t<0 ",",
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0 &"若 " t=0 ",",
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-infinity &"若 " t>0 ";") $
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infinity wide& t < 0,
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0 & t = 0,
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-infinity & t > 0) $
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#tab 以及
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$ t + infinity &= infinity + t = infinity + infinity = infinity "," \
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t + (-infinity) &= (-infinity) + t = (-infinity) + (-infinity) = -infinity "," \
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$ t + infinity &= infinity + t = infinity + infinity = infinity \
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t + (-infinity) &= (-infinity) + t = (-infinity) + (-infinity) = -infinity \
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infinity + (-infinity) &= (-infinity) + infinity = 0 $
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#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。
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