Mathematics is full of weird number systems that most people have never heard of and would have trouble even conceptualizing. But rational numbers are familiar. They’re the counting numbers and the fractions—all the numbers you’ve known since elementary school.
They’re the counting numbers and the fractions—all the numbers you’ve known since elementary school. But in mathematics, the simplest things are often the hardest to understand. They’re simple like a sheer wall, without crannies or ledges or obvious properties you can grab ahold of…
….Sets of numbers can have symmetry, too, and the more symmetry a set has, the easier it is to understand—you can apply symmetry relationships to discover unknown values. Numbers that have particular kinds of symmetry relationships form a “group,” and mathematicians can use the properties of a group to understand all the numbers it contains….
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