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set builder notation {4,8,12,16,....}

by A Lewis
(Austin, Texas)

The set shown below is an arithmetic sequence.

Rewrite the set in one of the common set builder notation formats.

Identify the Input Set, and the Output Function.


Comments for set builder notation {4,8,12,16,....}

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Aug 22, 2011
Set Builder Notation
by: Staff

The question:

by A Lewis
(Austin, Texas)


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.


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