Are all irrational numbers rational?

[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?

[CRGreathouse]

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.

[mathwonk]

????? are all humans non human? are all m ortals immortal? are al....

[fourier jr]

????? are all humans non human? are all m ortals immortal? are al....

lol :rofl:

[HallsofIvy]

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.