Set Builder Notation
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Set Builder Notation

by A Lewis
(Austin, Texas)

{4,8,12,16,....}

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Set Builder Notation

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Aug 22, 2011
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by: Staff

The question:

by A Lewis
(Austin, Texas)

{4,8,12,16,....}


The answer:

(Your Set of Numbers) S = {4,8,12,16,....}


Set "S" is the arithmetic sequence:

a_n = 4 + (n - 1) * (4)


the first 4 is the first term in the sequence

the second 4 is the difference between consecutive terms

a_n = is the nth term in the series (a with a subscript of n)

n = number of terms


There is more than one format for writing this sequence in Set Builder Notation.


Here is a commonly used format:


Set S = { 4 + 4(n - 1) | n ∈ ℕ, n ≥ 1 }


{} curly brackets surround the expression

∈ = element of a set

| and : can be used interchangeably. Both notations are separators which mean "where" or "such that"


4 + 4(n - 1) is the "output function"

n is the "variable"

ℕ (the set of all natural numbers) is the "input set"

n ≥ 1 is the "predicate"


Reading from left to right: "S" is the set of all numbers "4 + 4(n - 1)" where "n" is an element of the set of natural numbers ℕ and "n" is greater than or equal to 1.




Thanks for writing.

Staff
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