Introduction to Set Theory
The Set theory is a field of mathematics that studies sets. Sets are the collections of objects. However any kind of object can be collected into a set, the set theory is applied most frequently to objects which are relevant to mathematics. The set theory language can be used in the definitions of almost all mathematical objects.
The study of set theory was started by Georg Cantor and Richard Dedekind in the year 1870. Subsequent to the discovery of paradoxes in naive set theory, the number of axiom systems was proposed in the early 20th century.
Set theory is generally employed as a foundational system for mathematics, mostly in the form of Zermelo-Fraenkel set theory with the axiom of choice. Beyond the introductory role the set theory is a field of mathematics in its own right with an active research community. Contemporary research into set theory which includes a various collection of topics, varying from the structure of the real number line to the study of the consistency of large cardinals.
Table of set theory symbols
Symbol
Symbol Name
Meaning / definition
Example
{ }
set
a collection of elements
A={3,7,9,14}, B={9,14,28}
A ∩ B
intersection
objects that belong to set A and set B
A ∩ B = {9,14}
A ∪ B
union
objects that belong to set A or set B
A ∪ B = {3,7,9,14,28}
A ⊆ B
subset
subset has fewer elements or equal to the set
{9,14,28} ⊆ {9,14,28}
A ⊂ B
proper subset / strict subset
subset has fewer elements than the set
{9,14} ⊂ {9,14,28}
A ⊄ B
not subset
left set not a subset of right set
{9,66} ⊄ {9,14,28}
A ⊇ B
superset
set A has more elements or equal to the set B
{9,14,28} ⊇ {9,14,28}
A ⊃ B
proper superset / strict superset
set A has more elements than set B
{9,14,28} ⊃ {9,14}
A ? B
not superset
set A is not a superset of set B
{9,14,28} ? {9,66}
2A
power set
all subsets of A
? (A)
A = B
equality
both sets have the same members
A={3,9,14}, B={3,9,14}, A=B
Ac
complement
all the objects that do not belong to set A
A \ B
relative complement
objects that belong to A and not to B
A={3,9,14}, B={1,2,3}, A-B={9,14}
A - B
symmetric difference
objects that belong to A or B but not to their intersection
A={3,9,14}, B={1,2,3}, A ? B={1,2,9,14}
A={3,9,14}, B={1,2,3}, A ?B={1,2,9,14}
a∈A
element of
set membership
A={3,9,14}, 3 ∈ A
x∉A
not element of
no set membership
A={3,9,14}, 1 ∉ A
(a,b)
ordered pair
collection of 2 elements
A×B
Cartesian product
set of all ordered pairs from A and B
|A|
cardinality
the number of elements of set A
A={3,9,14}, |A|=3
#A
A={3,9,14}, #A=3
?
aleph
infinite cardinality
Ø
empty set
Ø = { }
C = {Ø}
U
universal set
set of all possible values
N0
natural numbers / whole numbers set (with zero)
N0 = {0,1,2,3,4,...}
0 ∈ N0
N1
natural numbers / whole numbers set (without zero)
N1 = {1,2,3,4,5,...}
6 ∈ N1
Z
integer numbers set
Z = {...-3,-2,-1,0,1,2,3,...}
-6 ∈ Z
Q
rational numbers set
Q = {x | x=a/b, a,b∈N}
2/6 ∈ Q
R
real numbers set
R = {x | -∞ < x <∞}
6.343434 ∈ R
C
complex numbers set
C = {z | z=a+bi, -∞<a<∞, -∞<b<∞}
6+2i ∈ C
Email based Set theory Homework Help -Assignment Help
Tutors at the www.tutorsglobe.com are committed to provide the best quality Set theory homework help - assignment help. They use their experience, as they have solved thousands of the set theory assignments, which may help you to solve your complex Set theory homework. You can find solutions for all the topics come under the set theory. The dedicated tutors provide eminence work on your Math homework help and devoted to provide K-12 level math to college level math help before the deadline mentioned by the student. Set theory homework help is available here for the students of school, college and university. Tutors Globe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
Qualified and Experienced Set theory Tutors at www.tutorsglobe.com
Tutors at the www.tutorsglobe.com take pledge to provide full satisfaction and assurance in Set theory homework help. Students are getting math homework help services across the globe with 100% satisfaction. We value all our service-users. We provide email based set theory homework help - assignment help. You can join us to ask queries 24x7 with live, experienced and qualified maths tutors specialized in set theory.
tutorsglobe.com the uncertainty principle assignment help-homework help by online atomic structure tutors
online ged exam preparation course and online ged tutoring package offered by www.tutorsglobe.com are the most comprehensive and customized collection of study resources on the web, offering best collection of ged practice papers, quizzes, ged test papers, and guidance.
www.tutorsglobe.com offers straight line depreciation homework help, straight line depreciation assignment help, online tutoring by accounting tutors.
nuclear reactor tutorial all along with the key concepts of classification of nuclear reactors, components of nuclear reactors,boiling-water reactor,pressurized-water reactor, fast breeder reactor
Introduction to the Systematic of Insects and Mites tutorial all along with the key concepts of Objectives of Classification, Elements of Classification, General Classification of Insects, Class Insecta, Subclass Apterygota, Subclass Pterygota and General Classification of Mites
tutorsglobe.com isoquants assignment help-homework help by online production function tutors
tutorsglobe.com accounting cost and economic cost assignment help-homework help by online cost concepts and categorization tutors
Free GMAT Study Guide, GMAT Test Papers, GMAT Practice papers, GMAT Test pattern and general information, Find GMAT exam information and resource, material free at Tutorsglobe.com
Fraunhofer Diffraction tutorial all along with the key concepts of Diffraction at a Single Slit, Observed Pattern, Diffraction by a circular aperture and Diffraction by a rectangular aperture
efficiency of algorithm depends on design and implementation of algorithm. algorithm uses computer resources to complete its task. an efficient algorithm is judged by the factor as to how economically and efficiently the cpu time and memory are used.
organic chemistry and classification of organic molecules tutorial all along with the key concepts of scope of organic chemistry, uniqueness of carbon atom, representation of organic molecules, classification of organic compounds, heterocyclic compounds
Theory and lecture notes of Creating Grouped Frequency Distributions all along with the key concepts of Lists and Statistics, STATS Key, STAT-EDIT, STAT-CALC, LIST Key, LIST-OPS, LIST-MATH. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Creating Grouped Frequency Distributions.
Refrigerators tutorial all along with the key concepts of Heat Pumps, Air conditioners, Coefficient of Performance of Refrigerators, Coefficient of Performance of Carnot-Cycle Refrigerator, Coefficient of Performance an Ideal Stirling-Cycle Engine
tutorsglobe.com photochemistry of retinal visual pigments assignment help-homework help by online receptor organs tutors
Introduction to Practical Chemistry IV tutorial all along with the key concepts of The range of experimental techniques, Organic chemistry, Criteria of Purity, Attitudes and Preparation, Safety precautions
1936580
Questions Asked
3689
Tutors
1450213
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!