Can two zeroes be equal?

Algebra Level 3

Which is greater?

$\huge 0^0 \ \text{or} \ 0^{0^0}$

0^0

Both are equal We can't find which is greater or lesser.

0^{0^0}

2 solutions

Satyabrata Dash
Mar 29, 2016

$0^0$ has indeterminate value, so $0^{0}$ and $0^{0^{0}}$ cant be compared for greater, lesser or equal values.

The calculator says 0^0^0=0 and 0^0=1

Rajdeep Bharati - 5 years, 2 months ago

Calculators are not trustworthy sometimes. They're programmed with different opinions. Some people say ${ 0 }^{ 0 }=0$ , some people say ${ 0 }^{ 0 }=1$ .

${ 0 }^{ 0 }$ is indeterminate. Proof:

$\lim _{ x\rightarrow 0 }{ { x }^{ 0 } } =1$

$\lim _{ x\rightarrow { 0 }^{ + } }{ { 0 }^{ x } } =0$

That makes ${ 0 }^{ { 0 }^{ 0 } }$ indeterminate as well.

You may also refer to this: What is 0 to the power of 0?

Kenneth Choo - 4 years, 11 months ago

no it doesnt. check out with a scientific calculator

Satyabrata Dash - 5 years, 2 months ago

I checked out with a scientific calculator and Rajdeep Bharati is true!

redouane rifki - 5 years, 1 month ago

@Redouane Rifki – Yes, me too

Rajdeep Bharati - 5 years, 1 month ago

Arulx Z
Mar 28, 2016

Value of $0^0$ is considered to be indeterminate

Can two zeroes be equal?

2 solutions

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