Question

2. 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.
a) the integers greater than 10
b) the odd negative integers
c) the integers with absolute value less than 1,000,000
d) the real numbers between 0 and 2
e) the set A × Z+ where A = {2, 3}
f ) the integers that are multiples of 10

Answer 1

Need help?

Answer 2

Yes

Answer 3

Please :(

Answer 4

First, do you know which are countably infinite and which aren't?

Answer 5

only letter e, i managed to do the rest

Answer 6

Have you done the 1-to-1 correspondence part for the others?

Answer 7

yes, i have

Answer 8

So every part of the question is solved except for "e"?

Answer 9

What do you know what the set from "e"? Tell me everything you know...

Answer 10

well if there is 2, it will be the double of every positive number and with 3 the triple but it wil still be positive integers?

Answer 11

Wait, is that what they're asking?

Answer 12

Or are they asking for a set of 2-tuples?

{ (2,1), (3,1), (2,2), (3, 2), (2,3),...}

Answer 13

i dont get it, they just want to know if its contable, or uncontable or so n if its countable then to show the correspondence thats all right?

Answer 14

im confused i jsut need this answer so i can get some sleep, ims o tired xd

Answer 15

It looks countable to me since you could set it up as something like:
I was thinking something along the lines of:

If even:
\[n \rightarrow (2, \frac{ n }{ 2 })\]

If odd:
\[n \rightarrow (3, \frac{ n+1 }{ 2 })\]

Answer 16

i tihnk its countable too, i just didnt know how to prove it.

Answer 17

thank you