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asmani
- 105
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What's the problem with this trivial solution: n --> n'th prime.
Can you give an example?asmani said:When I googled what I found were mind boggling functions...
https://math.stackexchange.com/ques...nction-from-the-natural-numbers-to-the-primesKrylov said:Can 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".
The map is into and not onto, e.g. you don't hit any prime greater than three.asmani said:Can you give a counterexample?
A bijective function is a type of function that has a one-to-one correspondence between its input and output. This means that each input has only one unique output, and each output has only one unique input.
A bijective function works by mapping each input value to a unique output value, and vice versa. This ensures that there are no duplicates in either the input or output set, creating a one-to-one correspondence.
A bijective function from naturals to primes is significant because it shows that the set of natural numbers can be mapped to the set of prime numbers in a one-to-one manner. This also means that the set of natural numbers and the set of prime numbers have the same cardinality.
A bijective function from naturals to primes can be useful in cryptography and number theory. It can also be used to prove certain mathematical theorems and to study the properties of prime numbers.
Yes, there can be other bijective functions involving prime numbers. For example, a bijective function from primes to odd numbers, or from primes to even numbers. The key is to have a one-to-one correspondence between the input and output sets.