Question

comparati cardinalul multimii​

Answer 1

A = {x | x ∈ ℕ, 2¹⁸¹ < x ≤ 2¹⁸²}

B = {y | y ∈ ℕ, 3¹²⁰ < y ≤ 3¹²¹}

card(A) = 2¹⁸² - 2¹⁸¹

= 2¹⁸¹•(2-1) = 2¹⁸¹ =

= 2¹⁸⁰•2 = (2³)⁶⁰•2 =

= 8⁶⁰•2

card(B) = 3¹²¹ - 3¹²⁰ =

= 3¹²⁰•(3-1) = 3¹²⁰•2 =

= (3²)⁶⁰•2 =

= 9⁶⁰•2

Deoarece 8⁶⁰•2 < 9⁶⁰•2:

⇒ card(A) < card(B)