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Using Braces, Ellipsis and Digits
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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.

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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 key


Digits: the international place-value number system we use includes ONLY 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9



Thanks for writing.

Staff
www.solving-math-problems.com


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