Question

Are the following statements coutably infinite, finite, or uncountable?
1. Points in 3D(aka triples of real numbers)
2. The set of all functions f from N to {a, b}
3. The set of all circles in the plane
4. Let R be the set of functions from N to R which are θ(n^3)

Answer 1

The answer is

1 Points in 3D --- uncountably infinite /Finite

2.The set of all functions-- uncountably infinite

3.The set of all circles in the plane--- uncountable

4 . R =the set of functions from N to R which are θ(n^3) --   Uncountable

Cardinality in Maths

The quantity of items in a mathematical set is known as a set's cardinality. It may be limited or limitless. For instance, if set A has six items, its cardinality is equivalent to 6: 1, 2, 3, 4, 5, and 6. A set's size is often referred to as the set's cardinality. The modulus sign is used to indicate it on either side of the set name, |A|.

• A finite set is a set with a finite number of elements and is countable. An infinite set, on the other hand, has an infinite number of elements, and an infinite set may be countable or uncountable.

According to the cardinality a set can be identified as many types ,they are,

• Countable sets
• Uncountable Sets
• Power Set
• Finite Set
• Infinite Sets

To know more about cardinality of sets refer to : https://brainly.in/question/11552331

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