Thursday, December 17, 2009

Which has more elements, the set of whole numbers or the set of natural numbers? or equal?

Kindly include explanation. The fact that 0 is in the set of whole numbers and not in the set of natural numbers is not the answer according to my teacher. Also, saying that they are equal because the cardinality of both are infinite is not acceptable. This is not an easy question, I guess.Which has more elements, the set of whole numbers or the set of natural numbers? or equal?
Beware: different people use ';whole number'; to mean different things.





To me ';whole number'; means ';real number lacking a fractional part'; -- i.e. an integer. Thus to me, -1, -2, etc are whole numbers.





But other people define them to be the natural numbers or sometimes something else. You should be explicit.





But it makes no difference here to the answer (only to the details of why) because in every case you can put all the numbers in one set into a 1-1 association with the other set - which means that have the same cardinality.





[The only detail here is writing the particular associations between the two sets, which depends on what you mean by ';whole number';.]





Indeed, the number of rational fractions of the form x/y (y not equal to 0) is also exactly as big as the set of natural numbers for the same reason.Which has more elements, the set of whole numbers or the set of natural numbers? or equal?
obviously set of whole numbers. I dont know why ur mam shud oppose to 0. Bcoz set of whole nos = set of natural nos + set 0

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