I don't understand the problem. x and y are free, so you can choose x=y. Then obviously, f(x)=f(y). Then it should follow x=x xor c, thus c=0. Or did they forget to claim that x and y are different?
The problem is stated correctly. You are reading it incorrectly, but I am not sure how.
If c=0, then it says that f(x)=f(y) if and only if (<=>) x=y. In other words, for all x≠y, f(x)≠f(y). Thus the function is 1-to-1. This is a nontrivial property that is difficult to check.
It’s easy to do. Einstein did the same thing with E=mc2.
Equality is a matter of identity. Equivalence is a matter of behavior.
The speed of light is not an absolute constant as Einstein believed. C just represented the speed that light can travel as a relationship between energy and mass.
My favorite form of the equation is C equals the square root of energy divided by mass.
Behaviorally all that means is that as the energy to mass ratio goes up, the speed of light goes up. And as the mass to energy ratio goes up, the speed of light goes down. Hence time dilation, black holes, etc.
[+] [-] Gehinnn|5 years ago|reply
[+] [-] cedex12|5 years ago|reply
https://en.wikipedia.org/wiki/Simon%27s_problem
[+] [-] greeneggs|5 years ago|reply
If c=0, then it says that f(x)=f(y) if and only if (<=>) x=y. In other words, for all x≠y, f(x)≠f(y). Thus the function is 1-to-1. This is a nontrivial property that is difficult to check.
[+] [-] knlje|5 years ago|reply
[+] [-] rymohr|5 years ago|reply
It’s easy to do. Einstein did the same thing with E=mc2.
Equality is a matter of identity. Equivalence is a matter of behavior.
The speed of light is not an absolute constant as Einstein believed. C just represented the speed that light can travel as a relationship between energy and mass.
My favorite form of the equation is C equals the square root of energy divided by mass.
Behaviorally all that means is that as the energy to mass ratio goes up, the speed of light goes up. And as the mass to energy ratio goes up, the speed of light goes down. Hence time dilation, black holes, etc.