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The Integral and Fractional Parts

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 3½ is 3 and the fractional part of 3½ is ½.

When I say that half of three is one, mathematically I mean [3 ÷ 2] = [1½] = 1. So, if it bothers you when I write ½ ⋅ 3 = 1, then just know that what I mean is [½ ⋅ 3] = 1.
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