x - (x - floor(x)) == x truncated to an integer when x is an irrational number > 1: "x - floor(x)" is just the fractional part of x, so it's an irrational num

x - (x - floor(x)) == x truncated to an integer when x is an irrational number > 1: "x - floor(x)" is just the fractional part of x, so it's an irrational number which is not equal to x. Subtracting the fractional part from the original leaves only the integer part, which is obviously rational.