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Find the error
Topic Started: Dec 5 2007, 07:21 PM (327 Views)
Kasnyia
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Chairman of the Bank
more rational numbers I believe.
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Tristan da Cunha
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Science and Industry
I have been told that there are precisely the same number of integers as there are rational numbers. They are both equal to the same value of infinity.

However, there are infinitely more irrational numbers than there are rational numbers, even though there are an infinite number of rational numbers.

That is, the number of irrational numbers between 0 and 0.00000001 (or any arbitrarily small real number) is infinitely more than all the rational numbers that exist from 0 to infinity.

The exact reasons for all of this are far beyond my mediocre mind.
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Rhadamanthus
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Legitimist

Tristan da Cunha
Dec 7 2007, 02:47 PM
I have been told that there are precisely the same number of integers as there are rational numbers. They are both equal to the same value of infinity.

However, there are infinitely more irrational numbers than there are rational numbers, even though there are an infinite number of rational numbers.

That is, the number of irrational numbers between 0 and 0.00000001 (or any arbitrarily small real number) is infinitely more than all the rational numbers that exist from 0 to infinity.

The exact reasons for all of this are far beyond my mediocre mind.

This is correct. A couple years ago, I could have laid out the reasons for all those things. I probably still could, given enough time to think it through, but I don't have that luxury right now.
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New Harumf
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Bloodthirsty Unicorn
** Snickers **

New theories are throwing out the old "rules"!

Infinity is not what it seems, especially when you get to the infinately small. These new theories will eventually explain "EVERYTHING"! :D
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