**Question:**What set is in another class of infinity that is bigger than ℕ?**Explanation:**In the theory of infinite sets, the natural numbers (denoted by ℕ) form an infinite set. However, there are larger classes of infinity. For example, the set of real numbers (denoted by ℝ) is a larger infinity than the set of natural numbers. This concept was first introduced by the mathematician Georg Cantor, and it is explored in detail within the framework of set theory.Cantor showed that the cardinality (size) of the set of real numbers is strictly greater than the cardinality of the natural numbers. This means there are different "sizes" or "types" of infinity. The cardinality of the natural numbers is denoted by ℵ₀ (aleph-null), and the cardinality of the real numbers is denoted by c (the cardinality of the continuum). Cantor’s diagonal argument provides a proof that ℵ₀ < c, establishing that there are more real numbers than natural numbers, even though both sets are infinite.

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What set is in another class of infinity that is bigger than N?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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