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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]

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16 Apr 2006, 10:21
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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)

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16 Apr 2006, 10:46
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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16 Apr 2006, 10:54
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.....

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16 Apr 2006, 11:05
Thanks giddi77... its crystal clear now!

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18 Apr 2006, 00:41
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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18 Apr 2006, 00:48
1) What is 0! == 1
2) What is 0^0 == 1
3) Is Zero positive, negative or neither = Its NEITHER!

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18 Apr 2006, 00:50
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!

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18 Apr 2006, 18:43
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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19 Apr 2006, 07:55
Even I tried with scientific calculator and it says

"Result of function is undefined"

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19 Apr 2006, 10:06
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

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19 Apr 2006, 13:16
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?

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19 Apr 2006, 13:35
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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20 Apr 2006, 16:11
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

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20 Apr 2006, 17:43
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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20 Apr 2006, 18:48
1) 0! = 1.
2) 0^0 --> I think it's undefined.
3) Zero is neither positive nor negative.

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20 Apr 2006, 18:48
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# Few questions about Zero: 1) What is 0! (1?) 2) What is 0^0

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