text: The set of odd numbers, even numbers and whole numbers all have the same cardinality (that is, there is a bijection between them)\n\nThere is a bijection between the whole numbers and the odd numbers as follows:\n\nf(t)=2(t)+1; t an integer\nThis is injective since suppose f(t)=f(s).\nThen 2(t)+1=2(s)+1\n=>t=s\nIndeed, it is surjective, since any odd number can be written in the form 2(m)+1, where m is an integer (whole number), and thus f(m)=2(m)+1\n(a bijection is a function that is both injective and surjective, that is, it is 1-1 and onto)\n\nSimilarly with the even numbers:\nDefine g(t)=2t; t an integer\nThen this is injective, for suppose g(t)=g(s)\nThen we have 2t=2s=>t=s\nIndeed, it's surjective because any even number can be written as 2m, where m is an integer.  \nThus, for any 2m an even number, 2m=g(m).\n\nIn fact, each of these infinite sets are denumerable, that is, there is a bijection from the natural numbers into the set of the odd numbers, there is a bijection from the natural numbers into the set of even numbers and there is a bijection from the natural numbers into the integers.\n\nSo you could say that the infinite sets of odd numbers, even numbers and integers all contained the same "number" of elements, even though this "number" is actually an infinite number.