1.* Infinite sums and infinite products of cardinals are defined as follows: Let d; be cardinals, and pick D, with o(D;)
Posted: Tue Jul 12, 2022 12:06 pm
- 1 Infinite Sums And Infinite Products Of Cardinals Are Defined As Follows Let D Be Cardinals And Pick D With O D 1 (132.69 KiB) Viewed 48 times
1.* Infinite sums and infinite products of cardinals are defined as follows: Let d; be cardinals, and pick D, with o(D;) = d.. (For Edi, pick the Di's disjoint.) Then Ed; is the cardinal of U D₁, and II d; is the cardinal of the Cartesian product of the Di's. Let di, e; be cardinals with d; <e; for all i. Prove that Σd; < IIe.. (Observe that if every d; = 1 and every e; = 2 we get Theorem 6.) 2.* Prove that N > N. (Hint: By Exercise 1 we have W No + N₁ + + №n + < NON The left side is N; the right side ≤ סא No.)