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Yes, they can be put into a one-to-one correspondence. The size of both sets is what's called a "countable infinity".
The mode, I think is not always a number in the data set it represents, for example I have a set of numbers, 1,7,2,4,6. You'll put them in order; 1,2,4,6,7. And there is no number that is the mode. So, I believe that is correct.
anything can be put into it so... (-infinity,infinity)
Put it off to the right side of the number as R(x)
Put the number down, and after that count up how many others of that # there are, including the one you put down, and then put the number of how many others there are and put it in smaller print on the upper right side of the number. EX: 33+42= 43