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Octal (base 8) is a numeral system with eight as the base. In the decimal system, ... His work was intended as recreational mathematics, ...
"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]
In a positional numeral system, the radix (pl.: radices) or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal system (the most common system in use today) the radix is ten, because it uses the ten digits from 0 through 9.
For example, the base-8 numeral 23 8 contains two digits, "2" and "3", and with a base number (subscripted) "8". When converted to base-10, the 23 8 is equivalent to 19 10, i.e. 23 8 = 19 10. In our notation here, the subscript "8" of the numeral 23 8 is part of the numeral, but this may not always be the case.
In a positional base b numeral system (with b a natural number greater than 1 known as the radix or base of the system), b basic symbols (or digits) corresponding to the first b natural numbers including zero are used. To generate the rest of the numerals, the position of the symbol in the figure is used.
8 is a composite number and the first number which is neither prime nor semiprime. By Mihăilescu's Theorem , it is the only nonzero perfect power that is one less than another perfect power. 8 is the first proper Leyland number of the form x y + y x , where in its case x and y both equal 2.
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A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.