Obscura: The Integral and Fractional Parts In my last post ( Foundations-Halving ), you learned that when halving an odd digit, you should treat it like the next lowest even number. For example, in 30 ÷ 2 we treat half of 3 the same as half of 2. Formally, this is accomplished using the mathematical function known as "the integral part." The integral part of a  is written with brackets, [ a ],  and identifies the unique integer a –1 <  [ a ] ≤ a . Similarly, the fractional part is denoted with curly brackets, { a }, such that { a } = a  – [ a ]. For example, the integral part of 3 ½ is 3  and the fractional part of 3 ½ is  ½ . When I say that half of three is one, mathematically I mean [3 ÷ 2] = [1 ½] = 1 . So, if it bothers you when I write  ½  ⋅  3 = 1, then just know that what I mean is [ ½  ⋅  3] = 1.