SOLUTION: Recall the one-to-one and onto mapping of the set of natural numbers to the set of integers. We used this mapping to show that the integers were countably infinite. Find a function
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Question 1176880: Recall the one-to-one and onto mapping of the set of natural numbers to the set of integers. We used this mapping to show that the integers were countably infinite. Find a function, f(n) that gives the nth integer of the given mapping below. You may find it useful to know that the floor(x) of a number is the largest integer that is less than or equal to x. You may use the floor in your final answer.
Examples: floor(4.3) = 4
floor(10.789) = 10
floor(8) = 8
floor(-2.6) = -3
Mapping:
N Z
1 0
2 1
3 -1
4 2
5 -2
6 3
7 -3
... ... Answer by ikleyn(52786) (Show Source):
You can put this solution on YOUR website! .
Recall the one-to-one and onto mapping of the set of natural numbers to the set of integers. We used this mapping to show that the integers were countably infinite. Find a function, f(n) that gives the nth integer of the given mapping below. You may find it useful to know that the floor(x) of a number is the largest integer that is less than or equal to x. You may use the floor in your final answer.
Examples: floor(4.3) = 4
floor(10.789) = 10
floor(8) = 8
floor(-2.6) = -3
Mapping:
N Z
1 0
2 1
3 -1
4 2
5 -2
6 3
7 -3
~~~~~~~~~~~~~~~~~~~~~~~~~~
Use this function
f: N ---> Z from natural numbers (= positive integers) to all integers
f(1) = 0,
f(n) = * , n > = 2.
It maps
n 1 2 3 4 5 6 7 8 9. . . .
f(n) 0 1 -1 2 -2 3 -3 4 -4 . . .
and so on.
