The Last Answer, by Isaac Asimov

Murray said, “But the odd integers can be derived. If you divide every even integer in the entire infinite series by two, you will get another infinite series which will contain within it the infinite series of odd integers.”

For S={2,4,6,8...}

S/2={1,2,3,4,..}

I used to think the set of even integers is a subset of the natural numbers.Doesnt this suggest that the reverse (the set of natural numbers being a subset of even integers) is actually true?

Re: The Last Answer, by Isaac Asimov

#5

Post by biesnecker » Sat, Sep 27, 2014, 4:29 PM UTC

I read this every time it appears on the front page, and I enjoy it every time. Asimov remains an inspiration.

Re: The Last Answer, by Isaac Asimov

#6

Post by CurtMonash » Sat, Sep 27, 2014, 4:33 PM UTC

ColinWright wrote: post #2

People might want to read the comments from two of the previous submissions of this: https://news.ycombinator.com/item?id=1287594 https://news.ycombinator.com/item?id=5585646 In particular, there's a link to "The Last Question" http://www.multivax.com/last_question.html That's been submitted before too: https://hn.algolia.com/?q=the+last+question#!/story/sort_by_...

Even more relevant is the other Multivac story "All the Troubles of the World", as per http://en.wikipedia.org/wiki/All_the_Troubles_of_the_World

Re: The Last Answer, by Isaac Asimov

#7

Post by CurtMonash » Sat, Sep 27, 2014, 4:35 PM UTC

ekm2 wrote: post #4

Murray said, “But the odd integers can be derived. If you divide every even integer in the entire infinite series by two, you will get another infinite series which will contain within it the infinite series of odd integers.” For S={2,4,6,8...} S/2={1,2,3,4,..} I used to think the set of even integers is a subset of the natural numbers.Doesnt this suggest that the reverse (the set of natural numbers being a subset of…

No, not a subset, for no more reason than that 17 is a member of the latter set and not of the former one.

What you're seeing is a 1:1 correspondence between an infinite set (the natural numbers) and a proper subset of same (the even natural numbers).

Re: The Last Answer, by Isaac Asimov

#8

Post by pedrosorio » Sat, Sep 27, 2014, 4:35 PM UTC

ekm2 wrote: post #4

Murray said, “But the odd integers can be derived. If you divide every even integer in the entire infinite series by two, you will get another infinite series which will contain within it the infinite series of odd integers.” For S={2,4,6,8...} S/2={1,2,3,4,..} I used to think the set of even integers is a subset of the natural numbers.Doesnt this suggest that the reverse (the set of natural numbers being a subset of…

I think what you mean is you used to think that the set of non-negative even integers was "smaller" than the set of natural numbers. The reason you can do this is because the set of non-negative even integers has the same cardinality as the set of naturals (both are countably infinite): http://en.wikipedia.org/wiki/Cardinality

The same is true of the rational numbers, by the way. There is a famous proof of the fact that there are infinite sets with larger cardinality that the naturals (the reals for example): http://en.wikipedia.org/wiki/Cantor's_diagonal_argument

Re: The Last Answer, by Isaac Asimov

#9

Post by kordless » Sat, Sep 27, 2014, 4:43 PM UTC

It is the awareness that you are immortal that would lead to the desire to end things (assuming the concept actually exists). Logically, the voice is simply a conduit to the interconnection (nexus) of all entities. Being singley aware my own consciousness is immortal and that consciousness is also part of a greater whole are equally appealing and frightening to me. That duality is slightly puzzling and interesting.

Re: The Last Answer, by Isaac Asimov

#10

Post by RangerScience » Sat, Sep 27, 2014, 8:05 PM UTC

ColinWright wrote: post #2

People might want to read the comments from two of the previous submissions of this: https://news.ycombinator.com/item?id=1287594 https://news.ycombinator.com/item?id=5585646 In particular, there's a link to "The Last Question" http://www.multivax.com/last_question.html That's been submitted before too: https://hn.algolia.com/?q=the+last+question#!/story/sort_by_...

One of those linked this:

http://localroger.com/prime-intellect/mopiall.html

which was :woah: