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I noticed that M04 has a couple of questions around 0's and

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I noticed that M04 has a couple of questions around 0's and [#permalink] New post 31 Jul 2008, 00:37
I noticed that M04 has a couple of questions around 0's and I screwed them up

Here's what I know about 0's

0 = even
0 is not negative, nor is it positive
0! = 1 (for whatever reason)
0^-1 = undefined (because it is 1/0)

But what is 0^0?
Is it 1 or is it 0?

MGMAT book says
"By definition, any base raised to 0 power yields 1"
and
"Any exponent expression with a base of 0 always yields 0, regardless of exponent"

I know this may be simple for some, but I never learned this.
Thanks for your help
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Re: Number property: Zero [#permalink] New post 31 Jul 2008, 03:15
fwl200 wrote:
But what is 0^0?
Is it 1 or is it 0?

MGMAT book says
"By definition, any base raised to 0 power yields 1"
and
"Any exponent expression with a base of 0 always yields 0, regardless of exponent"

I know this may be simple for some, but I never learned this.
Thanks for your help


No, it's not simple even for mathematicians. There's debate about how 0^0 should be defined; some think it should be defined to be equal to 1, but normally it's considered to be undefined (because, if you know calculus, limit(x -> 0) x^0 = 1, while limit(x -> 0) 0^x = 0).

So the MGMAT book is incorrect, if you've quoted it accurately- they should leave out the case of 0^0. Not that it matters on the GMAT- you'll never encounter this exceptional case on the test.
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Re: Number property: Zero [#permalink] New post 01 Aug 2008, 00:01
IanStewart wrote:
fwl200 wrote:
But what is 0^0?
Is it 1 or is it 0?

MGMAT book says
"By definition, any base raised to 0 power yields 1"
and
"Any exponent expression with a base of 0 always yields 0, regardless of exponent"

I know this may be simple for some, but I never learned this.
Thanks for your help


No, it's not simple even for mathematicians. There's debate about how 0^0 should be defined; some think it should be defined to be equal to 1, but normally it's considered to be undefined (because, if you know calculus, limit(x -> 0) x^0 = 1, while limit(x -> 0) 0^x = 0).

So the MGMAT book is incorrect, if you've quoted it accurately- they should leave out the case of 0^0. Not that it matters on the GMAT- you'll never encounter this exceptional case on the test.
You are right, the number is actually undefined.

But for that matters, 0^0 is often said in maths to be equal to 1. That is what solved most of the "issues" with this number. But this is just a convention and you should never really find this in the GMAT.
Re: Number property: Zero   [#permalink] 01 Aug 2008, 00:01
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I noticed that M04 has a couple of questions around 0's and

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