Determine whether each of these sets is countable or uncountable. For those that

Question

Determine whether each of these sets is countable or uncountable. For those that are countable, exhibit a one-to-one correspondence between the set of natural numbers and that set For example: Integers greater than 5: Countable   f(n)=n+5 1.) odd negative integers 2.) real numbers between 0 and 0.1 -Thanks in advance Determine whether each of these sets is countable or uncountable. For those that are countable, exhibit a one-to-one correspondence between the set of natural numbers and that set For example: Integers greater than 5: Countable   f(n)=n+5 1.) odd negative integers 2.) real numbers between 0 and 0.1 -Thanks in advance

Explanation / Answer

Dear User, a) Odd negative integers are countable based on this formula                            f(n)= -(2n+1)
b)   A set X is countable if its elements are counted in some order as we count the natural numbers. A set which is not countable is said to be uncountable. Uncountable sets are obviously infinite. Naturally, among infinite sets, countability or uncountability can be used as a tool to compare the infinitudes.
A set X is countable if its elements are counted in some order as we count the natural numbers.
A set X is said to be countable if X is either finite or all of its elements can be labelled (or enumerated ) as x1 , x2,

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