For an infinite cardinal number α, prove that α.α=α. , Advance Set Theory by I.Kaplansky

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For any finite cardinal number n prove that n+α=α , where α=#(ℕ) ,Advance Set Theory by I.Kaplansky For any finite cardinal number n prove that n+α=α , where α=#(ℕ) ,Advance Set Theory by I.Kaplansky
For any infinite cardinal number β , prove that α+β=β , where α=#(ℕ). Advance Set Theory For any infinite cardinal number β , prove that α+β=β , where α=#(ℕ). Advance Set Theory
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