Your Algebra Homework Can Now Be Easier Than Ever!

Basic Concepts of Set Theory

• Terminology
 • Set: a collection of objects
 • Element or Member of a set: an object belonging to the set

 • Three ways to designate sets:
  • word description
ex: the set of odd counting numbers between 2 and 12
  • the listing method
ex: {3, 5, 7, 9, 11}
  • set-builder notation
ex: {x | x ∈N, x is odd, and x < 12}

• Notes:
 • use curly braces to designate sets,
 • use commas to separate set elements
 • the variable in the set -builder notation doesn’t have to be x.
 • use ellipses (. . . ) to indicate a continuation of a pattern
established before the ellipses
ex: {1, 2, 3, 4, . . . , 100}

Important Number Sets

• N Natural or Counting numbers: {1, 2, 3, . . . }
• W Whole Numbers: {0, 1, 2, 3, . . . }
• I Integers: {. . . , -3, -2, -1, 0, 1, 2, 3, . . . }
• Q Rational numbers :
- Real Numbers : { x | x is a number that can be written as a
decimal }
• Irrational numbers: { x | x is a real number and x cannot be
written as a quotient of integers }.
Examples are:
Empty Set: { }


The symbols { x | x . . . } is read "x such that x . . . has some
The symbol ∈means is "an element of"
• Any rational number can be written as either a
TERMINATING decimal ( like 0.5, 0.333, or 0.8578966)
or a
REPEATING decimal ( like
• The decimal representation of an irrational number never
terminates and never repeats
• The set { } is not empty, but is a set which contains the empty

Set Cardinality

• Cardinality of a set: the number of distinct elements in the set
• textbook: n(A) - or we can use |A|
• If the cardinality of a set is a particular whole number, we call
that set a finite set
• If a set is too large to ever finish the counting process, it is called
an infinite set

• Well-Defined set: one for which we can determine membership,
i.e., given any arbitrary value we can determine conclusively
whether or not that value is in the set

Set Membership

• Well-Defined means that given a set and an object, we can
determine if the set contains that object

Set Equality

• Set Equality: the sets A and B are equal (written A = B) provided:
• every element of A is an element of B, and
• every element of B is an element of A
i.e., if they contain exactly the same elements

Prev Next

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:

OR is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for visitors -- if you order Algebra Helper by midnight of January 20th you will pay only $39.99 instead of our regular price of $74.99 -- this is $35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from for a 1$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

  • simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
  • factoring and expanding expressions
  • finding LCM and GCF
  • (simplifying, rationalizing complex denominators...)
  • solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
  • solving a system of two and three linear equations (including Cramer's rule)
  • graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
  • graphing general functions
  • operations with functions (composition, inverse, range, domain...)
  • simplifying logarithms
  • basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
  • arithmetic and other pre-algebra topics (ratios, proportions, measurements...)


Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:

OR is an authorized reseller
of goods provided by Sofmath
Check out our demo!
"It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..."
C. Sievert, KY
19179 Blanco #105-234
San Antonio, TX 78258
Phone: (512) 788-5675
Fax: (512) 519-1805

Home   : :   Features   : :   Demo   : :   FAQ   : :   Order

Copyright © 2004-2022, Algebra-Answer.Com.  All rights reserved.