標題: [Maths]Some questions about infinity [打印本頁] 作者: Kimo 時間: 18/11/2005 09:36 PM 標題: [Maths]Some questions about infinity 1) Whether 1/2^1 + 1/2^2 + 1/2^3 + ...... can written by 1, 1-1/∞ or 1-1/2^∞ ? 2) Is any number divided by 0 equal to ∞ ? 3) Can any number divided by 0 written by ∞ ? 4) If 1 + 2 + 3 + ...... written by ∞ or ∞(∞+1)/2, which is better ? 5) If ∞ power of any whole integer, is it equal to ∞ ? 6) Is 1/∞ = 0 ?
PS. Please give a reason when you answer above questions, thanks.
[ Last edited by Kimo on 2005-11-18 at 09:40 PM ]作者: 抹茶可樂 時間: 18/11/2005 11:13 PM Those are very incorrect concepts concerning infinity.
∞ cannot be directly added, multiplied or something else. It is not a number but symbol only. But we have somthing called limit, which can predict the trend of an expression when a variable tends to a certain value, but not exactly.