Minkowski's question-mark function

Minkowski's question-mark function is a special math tool that helps us measure how close a number is to being an integer.

So imagine you have a number like 3.2. That's not a whole number, but it's pretty close to the integer 3. However, if you have a number like 3.8, it's also not a whole number, but it's much closer to 4 than it is to 3.

Minkowski's question-mark function helps us measure that closeness. Specifically, it tells us how close a number is to being an integer based on its fractional part. The fractional part is the part of the number to the right of the decimal point.

So for example, if we want to know how close the number 3.2 is to being an integer, we would look at its fractional part, which is 0.2. Minkowski's question-mark function would tell us that the closeness value is 0.2, because 0.2 is closer to 0 than it is to 1.

Similarly, if we look at the number 3.8, its fractional part is 0.8. Minkowski's question-mark function would tell us that it's closer to 1 than it is to 0, so the closeness value is 0.2.

Overall, Minkowski's question-mark function helps us understand how close a number is to being a whole number, based on its decimal/fractional value.