Set-builder notation for ℕ > 11

set builder notation

Set-builder notation describes a set by stating the properties that all of the elements in the set must have.

Write the set using set builder notation (natural numbers greater than 11).

Comments for Set-builder notation for ℕ > 11

 Sep 04, 2012 Set-builder notation by: Staff Answer: Set “S” = the set of natural numbers greater than 11. (Natural numbers are whole counting numbers. Natural numbers do not include decimals or fractions.) Four different ways of representing set S are shown below: 1. ROSTER Notation 2. SET BUILDER Notation 3. INTERVAL Notation 4. GRAPHICAL Representation 1. ROSTER Notation: S = {12, 13, 14, 15, …} The first four elements (12, 13, 14, and 15) establish the pattern, and the ellipsis (three dots) shows that the pattern continues indefinitely. 2. SET BUILDER Notation: There is more than one format for writing this sequence in Set Builder Notation. Here is a commonly used format: S = {n | n ∈ ℕ, n > 11} {} curly brackets surround the expression ∈ = element of a set | and : can be used interchangeably. Both notations are separators which mean “where” or “such that” n: the first “n” is the “output function”, shown as = {n | n: the second “n” is the “variable”, shown as | n ∈ N, ℕ (the set of all natural numbers) is the“input set” n > 11 is the “predicate” Reading from left to right: “S” is the set of all numbers “n” {n | … , …} where “n” is an element of the set of natural numbers ℕ { … | n ∈ ℕ, … } and “n” is greater than 11 {… | … , n > 11}. 3. INTERVAL Notation: S = [12 . . ∞) This is an “unbounded interval”. The endpoint of 12 is included in the interval, but the endpoint ∞ is not included in the interval. Therefore [ ) must be used to show the interval. However, this notation CANNOT BE USED: S = [12, ∞). [12, ∞) means all REAL numbers which are greater than or equal to 12. Your set includes only INTEGERS. Your set does not include any other real numbers. Interval Notation for Integers should be written: S = [12 . . ∞) It should be read: the set of all natural numbers beginning with (and including) 12. 4. GRAPHICAL Representation: S = {12, 13, 14, 15, … } Thanks for writing. Staff www.solving-math-problems.com

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