※ 引述《mqazz1 (無法顯示)》之銘言：
: let R be a relation on a set A
: show that if R is reflexive and transitive,
: then R^n = R for all positive integer n
Also indution on n.
k
Assume that the R = R for k ≦ n.
n
Let (a,b) be in R. By assumption of induction, (a,b) is in R .
n+1
Since R is reflexive, (b,b) is in R, so (a,b) is in R .
n+1
Let (c,d) be in R . So there exist e is in A s.t.
n
(a,e) is in R , and (e,d) is in R. By assumption of induction,
(a,e) is in R . Since R is transitive, (a,d) is in R.
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煩請幫忙 第18046篇 #1CiVF51L (Math) [ptt.cc]
[分析] PDE 兩題 這一題 謝謝!!
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※ 編輯: sato186 來自: 111.242.8.225 (10/12 23:04)