# Using Braces, Ellipsis and Digits

by Sheila
(Portage, IN)

Please show problmen on how to use braces, ellipsis and digits to illustrate the set of negative even numbers.

### Comments for Using Braces, Ellipsis and Digits

 Sep 04, 2011 Using Braces, Ellipsis and Digits by: Staff The question:by Sheila (Portage, IN)Please show problmen on how to use braces, ellipsis and digits to illustrate the set of negative even numbers.The answer: You have asked a good question.You can illustrate ANY SET of objects (numbers or other objects) using set braces.For example, the following objects can form a set: knives, forks, and spoons.Set of silverware = {knives,forks,spoons} If the set is a group of numbers such as 1,6,21,0:Set of numbers = {1,6,21,0}Inserting an ellipsis into the set notation means: (1) Information has been omitted intentionally to save space; and/or (2) to show that an established pattern continues.The answer to your question is:Set of all negative even numbers = {. . .,-8,-6,-4,-2}For your information, this set can also be expressed as:Set of negative even numbers = { -2n | 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"-2n 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: The set of all negative even numbers "-2n" where "n" is an element of the set of natural numbers ℕ and "n" is greater than or equal to 1.Some Definitions:{ }, set braces (also called "curly brackets")[ ], square brackets (also called "box brackets")( ), Parentheses (also called "round brackets")Ellipsis: …, horizontal ellipsis along bottom of line. To type, hold down the "alt" key, type 0133, then release the alt key⋮, vertical ellipsis. To type, hold down the "alt" key, type 8942, then release the alt key⋰, UP RIGHT DIAGONAL ELLIPSIS. To type, hold down the "alt" key, type 8944, then release the alt key⋱, DOWN RIGHT DIAGONAL ELLIPSIS. To type, hold down the "alt" key, type 8945, then release the alt keyDigits: the international place-value number system we use includes ONLY 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9Thanks for writing.Staff www.solving-math-problems.com