Ni nini uthibitisho kwamba kuna idadi mbili irrational ambapo kuongeza moja kwa nguvu ya mwingine inazalisha idadi rational?
Hapa ni uthibitisho kwa kesi kwamba kuna kuna idadi mbili irrational a na b vile kwamba a ^ b ni rational. Kwanza, fikiria a = b = sqrt ((2). Kumbuka kwamba sqrt ((2) ni irrational, hivyo kama a ^ b = sqrt ((2) ^ sqrt ((2) ni rational, sisi ni kufanyika kwa sababu sisi kupatikana irrational a na b na a ^ b kuwa idadi rational. Vinginevyo, sqrt ((2) ^ sqrt ((2) ni irrational. Hebu a = sqrt ((2) ^ sqrt ((2) na b = sqrt ((2). Kisha a ^ b = (sqrt(2) ^ sqrt(2)) ^ sqrt(2) = sqrt(2) ^ (sqrt(2) * sqrt(2)) = sqrt(2) ^ 2 = 2, ambayo ni ya busara. Kwa hiyo njia yoyote, tunaweza kupata irrational a na b na a ^ b kuwa rational.