Nunbuh_Chrubble said:

The task is:

"define a one-to-one mapping from the set of natural numbers (N) onto the set of positive rational numbers (Q+)"

So making a 1-1 mapping from N to Q+ is a no-brainer... but making it "onto" throws me for a loop.

I remember how to prove that Q+ is countable:
Take a set Ap={n/p : n is an element of N} with p being an element of Z+, this is countable. Take the union of sets Ap from p=1 to p= infinity, this is equal to Q+. Since the union of countable sets is also countable, then Q+ is countable.

But I need to define an actual rule of correspondence between N and Q+...

I don't think I can use the union of countable sets thing above because each n from N corresponds to an infinite number of n/p, and so it is not unique, and therefor not a mapping.

Any advice?

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pfxtc said:

Math is so over my head it makes me giggle.

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isaacein said:

pfxtc said:

Math is so over my head it makes me giggle.

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What do you mean by "over your head"?

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pfxtc said:

People don't know what "over my head" means?

Guess you can be smart with one subject and dumb with another after all huh?

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DieCommie said:

Calculus for computer science is much easier than abstract algebra.  Fear not!

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DieCommie said:

This isnt science - its math! 

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Sure; and that white thing in the sky isn't a cloud, it's water!

Here's a nice problem for you. Evaluate



for a > 1.