Generalization of observation

Algebra Level 3

Observation :

0 π = 0 , 0 4.12 = 0 , 0 cos ⁡ 5 = 0 , 0 3 = 0 0^{\pi} = 0, 0^{4.12} = 0, 0^{\cos 5} = 0, 0^3 = 0 and 0 2190 = 0 0^{2190} = 0

but 0 0 0^0 is not defined.

Conclusion :

For all non zero real number n n , 0 n = 0 0^n = 0

Is the conclusion is true?

None of the choices All of the choices No Yes

Paul Ryan Longhas by Paul Ryan Longhas , 24, Philippines

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1 solution

Paul Ryan Longhas
Nov 27, 2015

Note that 0 n = 0 0^n = 0 iff n > 0 n > 0 .

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Yes Brilliant.

Kushagra Sahni - 5 years, 6 months ago

Yes, because for any n < 0 n<0 , 0 n = 1 0 n 0^n=\frac { 1 }{ { 0 }^{ n } } which is undefined.

Andy Wong - 5 years, 6 months ago

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