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It is imperative to understand that the type of numeration
system used to represent numbers has no impact upon the outcome of any
arithmetical function (addition, subtraction, multiplication, division,
roots, powers, or logarithms). A number is a number is a number; one plus
one will always equal two (so long as we're dealing with real
numbers), no matter how you symbolize one, one, and two. A prime number in
decimal form is still prime if it's shown in binary form, or octal, or
hexadecimal. π is still the ratio between the circumference and diameter of
a circle, no matter what symbol(s) you use to denote its value. The
essential functions and interrelations of mathematics are unaffected by the
particular system of symbols we might choose to represent quantities. This
distinction between numbers and systems of numeration is
critical to understand.
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