Basics

Algebra Level 3

True or false :

x x 0 x^x \geq 0

The equation above holds true for all non-negative integers x x .

False True

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2 solutions

The given condition satisfies all the natural numbers, but the thing mentioned in the question is for all non-negative integers, where non-negative integers are from 0 to 0 \text{ to } \infty . All the numbers satisfy except zero.

0 0 is not defined 0 \large \displaystyle \because 0^0 \text{is not defined} \ngeq 0 .

For natural numbers, x x 0 \large \displaystyle x^x \geq 0 .

Ashish Menon
Apr 27, 2016

0 0 0^0 is undetermined, so the equation does not hold for all non-negative integers. Hence the answer is false.

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