why 0<y1+y2<inf and 0<y2-y1<inf can be written as -y2<y1<y2 and 0<y2<inf
I need your help^^
maths! about the range?
2015-12-08 8:21 am
回答 (1)
2015-12-08 8:38 am
0 < y₁ + y₂ < ∞ ...... ①
0 < y₂ - y₁ < ∞ ...... ②
From ① (0 < y₁ + y₂), we have -y₂ < y₁
From ② (0 < y₂ - y₁), we have y₁ < y₂
Then, -y₂ < y₁ < y₂
① + ②：
0 < (y₁ + y₂) + (y₂ - y₁) < ∞
0 < 2y₂ < ∞
0 < y₂ < ∞
∴ -y₂ < y₁ < y₂ and 0 < y₂ < ∞
0 < y₂ - y₁ < ∞ ...... ②
From ① (0 < y₁ + y₂), we have -y₂ < y₁
From ② (0 < y₂ - y₁), we have y₁ < y₂
Then, -y₂ < y₁ < y₂
① + ②：
0 < (y₁ + y₂) + (y₂ - y₁) < ∞
0 < 2y₂ < ∞
0 < y₂ < ∞
∴ -y₂ < y₁ < y₂ and 0 < y₂ < ∞
收錄日期: 2021-04-18 14:08:51
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