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Symbols
Terminology
Sets of Numbers
Set Equivalence/ Set Equality
Misc./ Problems
100
Equals
What is the meaning of the symbol "="
100

A collection of objects

What is a set?

100
All numbers from 1 and up {1,2,3...}
What are natural numbers?
100
~
What is the symbol for set equivalence?
100
A set is so large that its cardinal number is not found among the whole numbers (it goes on forever)
What is an infinite set?
200
It means a set of numbers will be included inside
What is the meaning of these symbols, { }
200
An element is a member of the set.
What is an element?
200
All numbers from 0 up {0,1,2,3...}
What are whole numbers?
200
=
What is the symbol for set equality?
200
If the cardinal number of a set is a particular whole number it is a finite set.
What is a finite set?
300
It is the "an element of" symbol
What is this symbol ϵ
300
An empty set is a set containing no elements.
What is an empty set?
300
All negative and positive numbers and 0 {...-3,-2,-1,0,1,2,3...}
What are integers?
300
If every element of A is in B and every element of B is in A
How does A = B in set equality?
300

Is this set finite or infinite? {2, 4, 6, ... 32}

finite

400
It is the "not an element of" symbol
What is ∉
400
Math that deals with numbers in sets of units.
What is set theory?
400
Any number that can be written as a ratio of two integers with a nonzero denominator
What are rational numbers?
400
A ~ B is n(A) = n(B)
How does A ~ B in set equivalence?
400

Is this set finite or infinite? {x/x is a natural number greater than 50}

infinite

500
This is the "empty set" or "null set" symbol
What is ∅
500

Represents the number of elements in set A.

What is "number of elements or n(A)"?

500
Any number that can NOT be written as a ratio of two integers
What are irrational numbers?
500

Does {j,e,n} = {j,e,n,n,i,f,e,r} in set equality?

No, all of set B is not in set A.


500
In a well defined set it is possible to tell whether or not the element belongs to the set. In a not well defined set we cannot necessarily decide whether or not a given element belongs to the set.
What is the difference between a well defined and not well defined set?