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Math - the meaning of braces { }

by Marie
(Alabama)











































Grouping Symbols such as braces { } organize an algebra problem

Hello,

Can you please tell me what the brackets { } mean?

my e-mail is marie.xxxxx@us.army.mil


Thank you,

Marie xxxxxx

Comments for Math - the meaning of braces { }

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Sep 16, 2013
Curly Brackets { }
by: Staff


Answer

Part I


{ } are called curly brackets, or braces.
These symbols are used in two ways:

(1) to identify a set of elements.

(2) to group portions within a mathematical expression



Curley Brackets - also called Braces





{ } is used to identify a set of elements

Identifying a set using the { } symbols is used in the two of the most common set notation systems: a) ROSTER Notation, and b) SET BUILDER Notation.

Three examples of ROSTER Notation are shown below.


Consider a set of the following objects:

knife

fork

spoon

plate

cup

Using the ROSTER Notation { }, the set can be identified as:

{knife, fork, spoon, plate, cup}


Consider the set of all positive integers:

1

2

3

4

5

.
.
.


Using the ROSTER Notation { }, this set can written as:

{1, 2, 3, 4, 5, ...}


Consider the set of integers beginning with -3, and ending with + 3:

-3

-2

-1

0

1

2

3

Using the ROSTER Notation { }, this set can written as:

{-3, -2, -1, 0, 1, 2, 3}





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Sep 16, 2013
Curly Brackets { }
by: Staff


-------------------------------------------------------


Part II


Set Notation - identify the elements of eating utensils





Set Notation using Curly Brackets - identify the set of all positive integers







-------------------------------------------------------

Sep 16, 2013
Curly Brackets { }
by: Staff


-------------------------------------------------------


Part III


Set Notation using Curly Brackets - identify the set of all integers from -3 to +3, inclusive





{ } is used to group parts of a mathematical expression

Three of the most common symbols used to group portions of a mathematical expression are:

( ), parentheses - also called round brackets

[ ], square brackets - also called box brackets

{ }, curly brackets - also called braces

( ), [ ], and{ } can be interchanged with one another. They all mean the same thing.

The following expressions are equivalent to one another:

5(1 + 2) = 5[1 + 2] = 5{1 + 2} = 15


However, when a mathematical expression contains NESTED GROUPINGS, the ( ), [ ], and { } symbols are used to identify and separate those nested groupings.

The parentheses ( ) is generally used for the most inner brackets, the square brackets [ ] is used for the middle brackets, and the curly brackets { } is used for the outer brackets.

For example, the following expression contains nested groupings:

{[5(1 + 5) + 6]/3}

To evaluate this expression, the inner brackets ( ) will be evaluated first:

(1 + 5) = 6

The middle brackets [ ] will be evaluated second:

[5(1 + 5) + 6]

= [5(6) + 6]

= [30 + 6]


= 36


The outer brackets { } will be evaluated last:

{[5(1 + 5) + 6]/3}

= {[5(6) + 6]/3}

= {[30 + 6]/3}

= {36/3}

= 12



{[5(1 + 5) + 6]/3} = 12




-------------------------------------------------------

Sep 16, 2013
Curly Brackets { }
by: Staff


-------------------------------------------------------


Part IV



using Curly Brackets to group portions of a mathematical expression





using Curly Brackets to group portions of a NESTED mathematical expression








Thanks for writing.

Staff
www.solving-math-problems.com


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