Skip to main content
deleted 1 character in body
Source Link
Jada
  • 3
  • 2

I am looking for functions $f(x,y)$, real arguments, continuous, with the following properties:

  1. $f(m,n) = r$, where $r$ is integer $> 0$ if and only if $m,n$ are integers $> 0$.

  2. $f(m,n) \le f(r,s)$ if and only if $m n \le r s$, with $m,n,r,s$ integers $> 0$.

I would like to know if functions with properties 1 alone, 2 alone, or both together exist, and if they have been studied and given a specific name (for further investigation). In particular, I would be curious to know if relatively simple closed-form functions satisfying both conditions exist, or can exist at all. (If

If useful to restrict the scopeallow existence, the further constraints $m < n, r < s$ can be used.)

I am looking for functions $f(x,y)$, real arguments, continuous, with the following properties:

  1. $f(m,n) = r$, where $r$ is integer $> 0$ if and only if $m,n$ are integers $> 0$.

  2. $f(m,n) \le f(r,s)$ if and only if $m n \le r s$, with $m,n,r,s$ integers $> 0$.

I would like to know if functions with properties 1 alone, 2 alone, or both together exist, and if they have been studied and given a specific name (for further investigation). In particular, I would be curious to know if relatively simple closed-form functions satisfying both conditions exist, or can exist at all. (If useful to restrict the scope, the further constraints $m < n, r < s$ can be used.)

I am looking for functions $f(x,y)$, real arguments, continuous, with the following properties:

  1. $f(m,n) = r$, where $r$ is integer $> 0$ if and only if $m,n$ are integers $> 0$.

  2. $f(m,n) \le f(r,s)$ if and only if $m n \le r s$, with $m,n,r,s$ integers $> 0$.

I would like to know if functions with properties 1 alone, 2 alone, or both together exist, and if they have been studied and given a specific name (for further investigation). In particular, I would be curious to know if relatively simple closed-form functions satisfying both conditions exist, or can exist at all.

If useful to allow existence, the further constraints $m < n, r < s$ can be used.

added 24 characters in body
Source Link
Jada
  • 3
  • 2

I am looking for functions $f(x,y)$, real arguments, continuous, with the following properties:

  1. $f(m,n) = r$, where $r$ is integer $> 0$ if and only if $m,n$ are integers $> 0$.

  2. $f(m,n) \le f(r,s)$ if and only if $m n \le r s$, with $m,n,r,s$ integers $> 0$.

I would like to know if functions with properties 1 and/oralone, 2 alone, or both together exist, and if they have been studied and given a specific name (for further investigation). In particular, I would be curious to know if relatively simple closed-form functions satisfying both conditions exist, or can exist at all. (If useful to restrict the scope, the further constraints $m < n, r < s$ can be used.)

I am looking for functions $f(x,y)$, real arguments, continuous, with the following properties:

  1. $f(m,n) = r$, where $r$ is integer $> 0$ if and only if $m,n$ are integers $> 0$.

  2. $f(m,n) \le f(r,s)$ if and only if $m n \le r s$, with $m,n,r,s$ integers $> 0$.

I would like to know if functions with properties 1 and/or 2 exist, and if they have been studied and given a specific name (for further investigation). In particular, I would be curious to know if relatively simple closed-form functions satisfying both conditions exist, or can exist at all. (If useful to restrict the scope, the further constraints $m < n, r < s$ can be used.)

I am looking for functions $f(x,y)$, real arguments, continuous, with the following properties:

  1. $f(m,n) = r$, where $r$ is integer $> 0$ if and only if $m,n$ are integers $> 0$.

  2. $f(m,n) \le f(r,s)$ if and only if $m n \le r s$, with $m,n,r,s$ integers $> 0$.

I would like to know if functions with properties 1 alone, 2 alone, or both together exist, and if they have been studied and given a specific name (for further investigation). In particular, I would be curious to know if relatively simple closed-form functions satisfying both conditions exist, or can exist at all. (If useful to restrict the scope, the further constraints $m < n, r < s$ can be used.)

deleted 4 characters in body
Source Link
Jada
  • 3
  • 2

I am looking for functions $f(x,y)$, real arguments, continuous, with the following properties:

  1. $f(m,n) = r$, where $r$ is integer $> 0$ if and only if $m,n$ are integers $> 0$.

  2. $f(m,n) \le f(r,s)$ if and only if $m n \le r s$, with $m,n,r,s$ integers $> 0$.

I would like to know if functions with properties 1 and/or 2 exist, and if they have been studied and given a specific name (for further investigation). In particular, I would be curious to know if relatively simple closed-form functions satisfying both conditions exist, or can exist at all. (If useful to restrict the scope, the further constraints $m \le n, r \le s$$m < n, r < s$ can be used.)

I am looking for functions $f(x,y)$, real arguments, continuous, with the following properties:

  1. $f(m,n) = r$, where $r$ is integer $> 0$ if and only if $m,n$ are integers $> 0$.

  2. $f(m,n) \le f(r,s)$ if and only if $m n \le r s$, with $m,n,r,s$ integers $> 0$.

I would like to know if functions with properties 1 and/or 2 exist, and if they have been studied and given a specific name (for further investigation). In particular, I would be curious to know if relatively simple closed-form functions satisfying both conditions exist, or can exist at all. (If useful to restrict the scope, the further constraints $m \le n, r \le s$ can be used.)

I am looking for functions $f(x,y)$, real arguments, continuous, with the following properties:

  1. $f(m,n) = r$, where $r$ is integer $> 0$ if and only if $m,n$ are integers $> 0$.

  2. $f(m,n) \le f(r,s)$ if and only if $m n \le r s$, with $m,n,r,s$ integers $> 0$.

I would like to know if functions with properties 1 and/or 2 exist, and if they have been studied and given a specific name (for further investigation). In particular, I would be curious to know if relatively simple closed-form functions satisfying both conditions exist, or can exist at all. (If useful to restrict the scope, the further constraints $m < n, r < s$ can be used.)

deleted 6 characters in body
Source Link
Jada
  • 3
  • 2
Loading
Capitalise title
Source Link
LSpice
  • 12.9k
  • 4
  • 45
  • 69
Loading
deleted 24 characters in body
Source Link
Jada
  • 3
  • 2
Loading
deleted 4 characters in body
Source Link
Jada
  • 3
  • 2
Loading
added 28 characters in body
Source Link
Jada
  • 3
  • 2
Loading
Source Link
Jada
  • 3
  • 2
Loading