Q:

# What does 3 mean?

A:

The symbol 3 is a numeral representing the number that is three units larger than zero. The same concept can be written in other ways, such as writing "three" or using a tally to write "|||."

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In mathematics, 3 is a member of the set of natural numbers, {0, 1, 2, 3, 4, 5, ...}, which can be constructed using the Peano axioms.

The Peano axioms begin with the statement that zero is a natural number and continues by stating that every natural number has a successor, which is also a natural number. Since zero is a natural number, its successor, denoted S(0), is also a natural number. Also, since S(0) is a natural number, S(S(0)) must be a natural number as well. Continuing in this fashion creates a set {0, S(0), S(S(0)), S(S(S(0))), S(S(S(S(0)))), S(S(S(S(S(0))))), ...}.

Since this notation quickly becomes cumbersome, digits and numerals are used to represent each successor. For example, S(S(S(0))) is denoted by 3.

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