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How is Bernard different from the other Alphas?
He is shorter than the other Alphas. He is referred to as "a square peg in a round hole"
What is the set of odd numbers less than 14?
In the ordinary sense, yes. In the sense of set theory, no. – Bernard May 27 '17 at 23:1 Infinite sets behave differently than finite sets. Consider the map f:N→O where O is the set of all odd numbers. This can be written as a bijection f(n)=2n−1 and they have the same cardinality (|N|=|O|) – Dando18 May 27 '17 at 23:2 Also a question to think about: if two sets are infinite, than how is one larger than the other? What constitutes their size? This is why we look at the density and countability of sets. – Dando18 May 27 '17 at 23:2 Take the integers and the even integers (since they are a group and subgroup whereas the odds are not). If you defined "larger" to mean index bigger tha, then Z would be larger, [Z:2Z]=2, but in terms of cardinality both sets are the same size. They can be put in 1-1 correspondence with each other. – sharding4
