- #1

- 105

- 0

## Main Question or Discussion Point

What's the problem with this trivial solution: n --> n'th prime.

- I
- Thread starter asmani
- Start date

- #1

- 105

- 0

What's the problem with this trivial solution: n --> n'th prime.

- #2

fresh_42

Mentor

- 12,343

- 8,727

None.

- #3

S.G. Janssens

Science Advisor

Education Advisor

- 862

- 624

Can you give an example?When I googled what I found were mind boggling functions...

Your solution does of course use the result that the number of primes is not finite, so depending on what can be assumed known, that solution may not be "trivial".

- #4

- 105

- 0

https://math.stackexchange.com/questions/1160411/is-there-a-one-to-one-function-from-the-natural-numbers-to-the-primesCan you give an example?

Your solution does of course use the result that the number of primes is not finite, so depending on what can be assumed known, that solution may not be "trivial".

- #5

- 105

- 0

I was thinking about bijection from Q to N. here is what I came up with: m/n --> 2^{m}3^{n}

And it's easy to show there's a bijection from the set "2^{m}3^{n} for all coprime n and m" to N.

Edit: This is Q+ to N. Does it work?

And it's easy to show there's a bijection from the set "2

Edit: This is Q+ to N. Does it work?

Last edited:

- #6

fresh_42

Mentor

- 12,343

- 8,727

It's an embedding (injective), but is is no surjection.

- #7

- 105

- 0

Can you give a counterexample?

- #8

fresh_42

Mentor

- 12,343

- 8,727

The map is into and not onto, e.g. you don't hit any prime greater than three.Can you give a counterexample?

- #9

- 105

- 0

Here is the bijection from W to N: Map the smallest member of W to 1, the second smallest member of W to 2, and so on

- #10

fresh_42

Mentor

- 12,343

- 8,727

Here's an interesting paper about the repetitions in it:

http://www.cs.utexas.edu/users/sandip/acl2-09/presentations/rationals-talk.pdf

- Last Post

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 5

- Views
- 19K

- Last Post

- Replies
- 1

- Views
- 1K

- Replies
- 3

- Views
- 9K

- Replies
- 2

- Views
- 2K

- Replies
- 8

- Views
- 4K

- Replies
- 0

- Views
- 3K