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# Few questions about Zero: 1) What is 0! (1?) 2) What is 0^0

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Few questions about Zero: 1) What is 0! (1?) 2) What is 0^0 [#permalink]  16 Apr 2006, 09:21

1) What is 0! (1?)
2) What is 0^0 (non-existent?)
3) Is Zero positive, negative or neither (I would guess that last choice)
VP
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Re: Zero [#permalink]  16 Apr 2006, 09:46
ashkapoo wrote:

1) What is 0! (1?)
2) What is 0^0 (non-existent?)
3) Is Zero positive, negative or neither (I would guess that last choice)

Yes 0! = 1
0^0 is cannot be determined.
Zero is neither positive nor negative

A few more: (Disclaimer: Use these @your own risk. These are based on what I found from the web)
Zero is even
For any integer k, k^0 = 1
Zero is divisible by every integer (except 0), Since remainder of 0/k = 0
Zero is a multiple of every integer. 0 = k*0
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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

VP
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Re: Zero [#permalink]  16 Apr 2006, 09:54
giddi77 wrote:
ashkapoo wrote:

1) What is 0! (1?)
2) What is 0^0 (non-existent?)
3) Is Zero positive, negative or neither (I would guess that last choice)

Yes 0! = 1
0^0 is cannot be determined.
Zero is neither positive nor negative

A few more: (Disclaimer: Use these @your own risk. These are based on what I found from the web)
Zero is even
For any integer k, k^0 = 1
Zero is divisible by every integer (except 0), Since remainder of 0/k = 0
Zero is a multiple of every integer. 0 = k*0

agree with whole heart.....
Intern
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Thanks giddi77... its crystal clear now!
Manager
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Kudos [?]: 2 [0], given: 0

One reason why 0^0 is not determinable could be explained in this fashion -
0^0 = 0^x/0^x (x not equal to 0) = 0/0 (which is indeterminable).
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Thanks,
Zooroopa

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Re: Zero [#permalink]  17 Apr 2006, 23:48
1) What is 0! == 1
2) What is 0^0 == 1
3) Is Zero positive, negative or neither = Its NEITHER!
VP
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Zooroopa wrote:
One reason why 0^0 is not determinable could be explained in this fashion -
0^0 = 0^x/0^x (x not equal to 0) = 0/0 (which is indeterminable).

Its is determinable!! Try entering it in a scientific calculator (windows calculator has scientific mode) you will get 1!

And, yeah ur logic is correct!
Manager
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sm176811 wrote:
Zooroopa wrote:
One reason why 0^0 is not determinable could be explained in this fashion -
0^0 = 0^x/0^x (x not equal to 0) = 0/0 (which is indeterminable).

Its is determinable!! Try entering it in a scientific calculator (windows calculator has scientific mode) you will get 1!

And, yeah ur logic is correct!

The scientific calculators that I had, when I was a child, did not give 1!!!
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Thanks,
Zooroopa

Senior Manager
Joined: 24 Jan 2006
Posts: 252
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Even I tried with scientific calculator and it says

"Result of function is undefined"
VP
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gmatacer wrote:
Even I tried with scientific calculator and it says

"Result of function is undefined"

of 0!?

Seem to work for me on Windows and Casio 991fx
Manager
Joined: 04 Jan 2006
Posts: 58
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Kudos [?]: 1 [0], given: 0

Can somebody explain this?
Zero is divisible by every integer (except 0), Since remainder of 0/k = 0

Suppose 0/2
Quotient 0 and reminder 2.
Is this right?
Senior Manager
Joined: 15 Mar 2005
Posts: 419
Location: Phoenix
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Nayan wrote:
Can somebody explain this?
Zero is divisible by every integer (except 0), Since remainder of 0/k = 0

Suppose 0/2
Quotient 0 and reminder 2.
Is this right?

Nayan, in division,

Number = Divisor * Quotient + Remainder

In case of 0/2, Number = 0, Divisor = 2.
Since 0 = 2*0 + 0, we have Quotient = 0 and Remainder = 0.

Does that help?
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Who says elephants can't dance?

Intern
Joined: 12 Dec 2005
Posts: 10
Location: Singapore
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Kudos [?]: 0 [0], given: 0

0^0 is 1 because, any number to the power 0 is always 1.

For example 2^0 = 1; -1^0 = 1; So is 0^0 = 1
Senior Manager
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sheetal wrote:
0^0 is 1 because, any number to the power 0 is always 1.

For example 2^0 = 1; -1^0 = 1; So is 0^0 = 1

Any number (excluding 0) has n^0 = 1 for this reason:
(its not an axiom, its a provable theorem).

n^2 = n^3/n
n^1 = n^2/n
n^0 = n^1/n = n/n = 1.

So 5^0 = 5/5 = 1.

0^0 is undefined.
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Who says elephants can't dance?

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5068
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Kudos [?]: 193 [0], given: 0

1) 0! = 1.
2) 0^0 --> I think it's undefined.
3) Zero is neither positive nor negative.
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# Few questions about Zero: 1) What is 0! (1?) 2) What is 0^0

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