What exactly is your difficulty? Do you know what "injection" and "surjection" mean? It should be very easy to do part (a) or part (c). Parts (b) and (d) are a little harder. Can you use the fact that , , and are all "countable" sets?
I need help! can someone help me with this?
Prove or disprove the following statements:
(a) There exists an injection fromN to N^2.
(b) There exists a surjection from N to N^2.
(c) There exists an injection from N to N^3.
(d) There exists a surjection from N to N^3.
where N is the set of natural numbers.
Thanks
You didn't anaswer HallsofIvy's last question.
Have you seen this before?
http://personal.maths.surrey.ac.uk/s...ntable.svg.png
Yes i made used of countability and also the picture. I solve for N^2 already. Is there a shortcut on N^3 such that we can make use of N^2? instead of using 3D space and come up with a general formula for the function? For example let F: N--> N^2 and G: N^2--->N3? so that f(x)=(x,y) and gf(x)=(x,y,z)?