Counting Elements in Sets
Main Questions:
- What is the number of elements in a set?
- When do two sets have the same number of elements?
We shall work with subsets of the positive integers
1,2,3,4,5, ...
How many elements are there in each of the following sets?
- {1,2,3,4,5,6}
- {2,4,6}
- {2,4,6,8,10,12}
- {4,6,8,10,12,14}
- {8,10,14}
How many elements are there in each of the following sets?
- {1,2,3,4,5, ... } (the set of all positive integers)
- {2,3,4,5, ... } (the set of all positive integers >= 2)
- {2,4,6,8,10, ...} (the set of all even positive integers)
- {10002,10004,10006,10008,100010, ...} (the set of all even positive integers >=1000 )
Do you know what a prime number is?
The first few positive primes are 2,3,5,7,11,13,17,19,23,29,31,... .
How many elements are there in each of the following sets?
- The set of all positive prime numbers
- The set of all positive prime numbers > 29
Of all the sets considered above, identify and group those which have the same number of elements.
Attempt a definition: The set A has the same number of elements as the set B if and only if ...
Using your definition, redo the question: Of all the sets considered above, identify and group those which have the same number of elements.
N.B. A positive integer p is a prime number if p is not 0 or 1 and if p is divisible only by 1 and p.
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