Pub Date : 2018-10-03DOI: 10.1201/9781315273761-36
J. N. Salunke, B. S. Satpute
For transfinite cardinal number α, using Zorn’s lemma we have given a simple proof which is understandable to undergraduate students, of the result α + α = αα = α, that is, idempotency for addition and multiplication. Moreover for a cardinal number with 2 ≤ < α we obtain easily α + = α = α, α = α α = 2 α , α < . Using these results we get many results directly as א0 + ∁ = א0∁ = ∁ + ∁ = ∁∁ = ∁, א0 א0 = ∁ = ∁0 = 20 , ∁ = א0 ∁ = 2 where א0 = card N, ∁ = card R. -------------------------------------------------------------------------------------------------------------------------------------Date of Submission: 05-08-2018 Date of acceptance: 22-08-2018 -------------------------------------------------------------------------------------------------------------------------------------
For transfinite cardinal numberα、使用佐恩引理we have给定a simple被一本可以证明当时本科学生,of the resultα+α=αα=α,that, idempotency除了和multiplication。tip for a cardinal号码与2≤<我们很容易地获取αα+=α=α,α=αα= 2α,α<。使用这些结果我们get many结果直接+ 0轴א∁=א∁=∁+∁=∁∁=∁,אא0 =∁=∁0 = 20,∁=א∁= 2 whereא0 = N,∁=卡R . ------------------------------------------------------------------------------------------------------------------------------------- 约会或屈服:05-08-2018约会或验收:8 -------------------------------------------------------------------------------------------------------------------------------------
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