Sizes of Infinity

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Sizes of Infinity

Post  theonlyMattinMathCounts on Mon Mar 09, 2009 7:45 am

Which of the following infinitely large sets is largest?

a.) the set of all rational numbers
b.) the set of all positive even numbers
c.) the set of all positive odd numbers
d.) the set of all real numbers from 0 to 1, inclusive
e.) the set of all counting numbers (1, 2, 3, 4, ...)
f.) All of the above sets are the same size.

If your answer is a-e, provide a proof as to why the set you chose is larger.

P.S.
Where am I getting these points from?

Here is the answer
Spoiler:
The answer is d. All other sets are countably infinite. This means that they can all be counted. The set of all real numbers from 0 to 1 inclusive has too many elements to be counted. The set starts with zero and then the next possible number is too small to be counted. It is pretty much 0.0000000000000000000...1 where ... is an infinite number of zeroes.


Last edited by theonlyMattinMathCounts on Sat Apr 11, 2009 12:26 am; edited 2 times in total (Reason for editing : Hehe)
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Re: Sizes of Infinity

Post  Ben R on Thu Mar 26, 2009 4:16 am

I'm probably wrong due to under thinking it, but...


Spoiler:
All of them are the same, EXCEPT A, which will total to 0. Only A includes negative numbers. All the rest add up to infinity, just at different rates.
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Meh

Post  theonlyMattinMathCounts on Sun Mar 29, 2009 8:04 am

Well I was actually talking about the number of numbers in the set not the sum of numbers.
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Re: Sizes of Infinity

Post  AK_Kadaveru on Sat Jan 09, 2010 11:21 pm

My answer is
Spoiler:
F, because they all are infinity

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