Question

Find a function f(x, y) that fits the following conditions:

1. f(x, y) only outputs values between (inclusive) 0 and 1 and is defined for all real x and y greater than or equal to 0
2. f(x, y) > 0.5 iff x > y
3. f(x, y) < 0.5 iff x < y
4. f(x, y) = 0.5 iff x = y
5. f(x, y) gets closer to zero faster as the difference between x and y gets greater (x < y)
6. f(x, y) gets closer to one faster as the difference between x and y gets greater (x > y)
7. f(x, y) = 1 iff x > 0 and y = 0
8. f(x, y) = 0 iff x = 0 and y > 0
9. f(x, y) is "close" to 0.5 iff x is "close" to y

Answer 1

Doesn't need to be in any specific form. As long as instructions are given on how to compute f(x, y) it'll work.