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How do you find out cardinality?
cardinality is the number of element in a set :) * * * * * The question did not ask what cardinality was but how to find it! For a simple set with a finite number of elements it is possible to count the number of distinct elements - even though it may be time consuming. For other finite sets, such as symmetry groups, it is not always easy to identify distinct elements before counting how many there are. However, there are theoretical methods that will help in such cases. The cardinality of an infinite group is Aleph-Null if it there is a 1-to-1 mapping with the set of integers. The cardinality is Aleph-One if the mapping is with the real numbers. If you go beyond that, you will have studied a lot more about cardinality and will not need to ask such a question!
Can you make an operator that takes any given irrational number and maps it onto the rationals?
Of course not.Number if irrational numbers is larger than number of rational numbers.To be more exact: There is no one-to-one mapping of set of rational numbersto the set of irrational numbers. If there would be such a mapping, their cardinality(see Cardinality ) would be same.In reality, rational numbers are countable (cardinality alef0)real numbers, as well as irrational numbers are not countable (cardinality alef1).These are topics inwikipedia.org/wiki/Transfinite_numbertheory
What are mapping cardinalities?
It's the number of mappings, *or* he number of available objects to map something to, *or*...See also http://en.wikipedia.org/wiki/Cardinality
How do you find the cardinality?
by counting the number of elements in a set. * * * * * For a simple set with a finite number of elements it is possible to count the number of distinct elements - even though it may be time consuming. For other finite sets, such as symmetry groups, it is not always easy to identify distinct elements before counting how many there are. However, there are theoretical methods that will help in such cases. The cardinality of an infinite group is Aleph-Null if it there is a 1-to-1 mapping with the set of integers. The cardinality is Aleph-One if the mapping is with the real numbers. If you go beyond that, you will have studied a lot more about cardinality and will not need to ask such a question!
What is the cardinality of the interval from zero to one including zero but not including one?
The cardinality of [0,1) is equal to the cardinality of (0,1) which has the same cardinality as the real numbers.
