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Are all irrational numbers rational?

 
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Aug30-06, 05:36 PM   #1
 

Are all irrational numbers rational?

Since pie is the ratio of the circumference of the circle to its diameter, isn't it possible that there exist a fraction for all nonrepeating going on forever decimal values?
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Aug30-06, 06:54 PM   #2
 
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Quote by Skhandelwal
Since pie is the ratio of the circumference of the circle to its diameter, isn't it possible that there exist a fraction for all nonrepeating going on forever decimal values?
Short answer: No.

Tongue-in-cheek answer: Yes, but the fraction would have at least one noninteger.

Longer answer: You're wrongly assuming that a circle with rational circumference and diameter exists.
Aug30-06, 10:18 PM   #3
 
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????? are all humans non human? are all m ortals immortal? are al....
Aug31-06, 03:02 AM   #4
 

Are all irrational numbers rational?

Quote by mathwonk
????? are all humans non human? are all m ortals immortal? are al....
lol
Aug31-06, 03:10 AM   #5
 
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Quote by Skhandelwal
Since pie is the ratio of the circumference of the circle to its diameter, isn't it possible that there exist a fraction for all nonrepeating going on forever decimal values?
The definition of "rational number" is that it can be written as a fraction with numerator and denominator integers. The "ratio of the circumference of the circle to its diameter" is not a ratio of integers.
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