Quote:
Originally Posted by Bilbo1967
First = eight?
Last = two?
Do you get infinity if you add them all up? Because there are an infinite number of positive integers?
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Yes to both. And yes, one answer is that the sum is infinite. It's certainly divergent. But see below.
Quote:
Originally Posted by Hamlet53
most common T
least common O ?
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Yes! And all because of ten! Although there's another argument that since there are an infinite number of numbers beginning O, N, F, S and T they are all equally common. However, I was thinking of the answers you gave.
Quote:
Originally Posted by Hamlet53
What's the last number in the list? There isn't one. As Bilbo notes there are an infinite number of positive integers.
Not sure what add them all up would mean either. Eight + ? + T + O = ?
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There are an infinite number of numbers in the list, but we can show that the last one is two by asking for a counter-example. There's no number that would come after two, so two must be the last one.
There are some branches of mathematics that try to deal with divergent series. In a very specific mathematical sense, the sum of all the positive integers is negative one twelfth. (-1/12). I confess I don't really understand that myself. Mathematics involving integers is tricky or even tricksy.
I award the win to Bilbo1967. Over to you, Bilbo.