英和和英

出典:『Wikipedia』 (2011/06/18 23:02 UTC 版)

英語による解説

引用

In abstract algebra a linearly ordered or totally ordered group is an ordered group G such that the order relation "≤" is total. This means that the following statements hold for all a, b, c ∈ G:

• if a ≤ b and b ≤ a then a = b (antisymmetry)
• if a ≤ b and b ≤ c then a ≤ c (transitivity)
• a ≤ b or b ≤ a (totality)
• the order relation is translation invariant: if a ≤ b then a + c ≤ b + c and c + a ≤ c + b.