Discrete Math Homework: Determine whether each of these sets is finite, countably inf

[zozc13]

Hello im having a little trouble with these problem.

1.Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set. For those that are not, explain your answer.
(a) The set of odd integers greater than or equal to 5.
(b) The set of all bit strings with 1 in the first two positions and 0 in all the other positions.
(c) The sets of all rational numbers between .5 and 1.
(d) The set of all real numbers between .5 and 1.
2. Is the function f(n) = -n from Z^- to Z⁺ (Where Z^-is the set of negative integers and Z⁺ is the set of positive integers)
(a) one-to-one? (b) onto? (c) a bijection?

 

[HallsofIvy]

Hello im having a little trouble with these problem.

1.Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set. For those that are not, explain your answer.
(a) The set of odd integers greater than or equal to 5.
(b) The set of all bit strings with 1 in the first two positions and 0 in all the other positions.
(c) The sets of all rational numbers between .5 and 1.
(d) The set of all real numbers between .5 and 1.

Okay, what "little trouble" are you having? Do you know what "finite", "countably infinite", and "uncountable" mean? Do you know what a "one-to-one correspondence" is? Since you have not shown any attempt to do these yourself we have no idea what kind of help you need.

2. Is the function f(n) = -n from Z^- to Z⁺ (Where Z^-is the set of negative integers and Z⁺ is the set of positive integers)
(a) one-to-one? (b) onto? (c) a bijection?

If you are asked a question like this, surely your text has definitions of "one-to-one", "onto", and "bijection". What are they?