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When is 0 / 0 =1 ? : Solution Posted

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When can the following be true?

0 / 0 = 1

Yes, read as zero divided by zero equals one!

No Tens, unit, magic.. blah blah! guess enuff hint for now

Finally the solution:

dBm is a unit to measure absolute Power, x dBm = 10* log(X^10e+3), where X is power in Watts.

Thus, 1 mw (milli Watt) = 10e-3 W = 10 * log(1) dBm = 0 dBm

Now, 0 (in dBm) / 0 (in dBm) = 1 (but Obvious)

So fellas, spot any fallacies?

Gee, should acknowledge some guy in SD for some funny questions on dBm scale which led to this q. Me thinks it makes cracker of a q

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Does it involve limits?

Like: lim(x->0) sin(x) / x = 1

Nopes, no limits please, but that's clever! Some non-linear ideas may help...

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a = 1

a = b

a^2 = ab

a^2 - b^2 = ab - b^2

(a+B.) (a-B.) = b(a-B.)

divide through by a-b

(a+B.) = b

a + b -1 = b-1

1 + 1 - 1 = 1-1

1 = 0

so

0/0 = 1

is the same as

0/1 = 0

and therefore the answer is always.

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The expontial value n^0= 1 then 0^0 = 1

Theefore if we write:

=> 0^0 / 0^0 = 1

=> 1 / / = 1

QED.

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=> 0^0 / 0^0 = 1

QED.

not indeed! 0^0 != 1

Take logarithm on both sides and it crashes to indeterminate form...

Well, but maybe on the right track

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a = 1

divide through by a-b

and therefore the answer is always.

Division by (a-B.) results in indeterminate form... but keep thinking!

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Yeah I know - I was kidding with that one. When I was in school one of my profs challenged us to prove 25 incorrect mathematical concepts such as ln 1 = 0; 0=1; i squared = 1;....

I won.

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Skale. This may not be the answer you were looking for but I stand by the mathematices of this.

The answer to any number to the power of 0 = 1.

(try typing the equation 0 to the power 0 (ie 0^0=) into google for example and see what answer it gives).

Texts on the matter call the equation, the 'indeterminate form'. But all perceived wisdom accepts 0^0=1

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Skale. This may not be the answer you were looking for but I stand by the mathematices of this.

The answer to any number to the power of 0 = 1.

(try typing the equation 0 to the power 0 (ie 0^0=) into google for example and see what answer it gives).

Texts on the matter call the equation, the 'indeterminate form'. But all perceived wisdom accepts 0^0=1

That's just bad programming which doesn't test the 0 base along with the 0 exponent. 0 raised to any non-negative exponent (except 0) is 0, and any number raised to the 0 power (except 0) is 1, but it's just easier to do those tests separately than together. So 0^0 ends up being 1, even though that's mathematically incorrect.

And Skale, if you know what an indeterminate form is, then you should also realize that 0/0 is also an indeterminate form. As is infinity/infinity, infinity - infinity, etc etc.

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That's just bad programming which doesn't test the 0 base along with the 0 exponent. 0 raised to any non-negative exponent (except 0) is 0, and any number raised to the 0 power (except 0) is 1, but it's just easier to do those tests separately than together. So 0^0 ends up being 1, even though that's mathematically incorrect.

And Skale, if you know what an indeterminate form is, then you should also realize that 0/0 is also an indeterminate form. As is infinity/infinity, infinity - infinity, etc etc.

Thanks, you are correct as to 0/0 by itself is indeterminate form... that is another hint! But you shall see when I reveal the answer (or unless someone thinks of it...). Btw, I have submitted it somewhere and yet to hear back on it!

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When can the following be true?

0 / 0 = 1

Yes, read as zero divided by zero equals one!

No Tens, unit, magic.. blah blah! guess enuff hint for now

The answer is never

He did not say that is was true - he asked when can it be true.

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The answer is never

He did not say that is was true - he asked when can it be true.

No, there is way! Am claiming a very neat and simple solution for this one..

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0 = 0 + 0 +0 + 0 + 0 +0 +0 ....

0 = (1 + -1)

0 = (1 + -1) + (1 + -1) +(1 + -1) ...

associtive property

0 = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1)....

-1 + 1 = 0

0 = 1 + 0 + 0...

0 = 1

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O = 1... O/O = 1... ta daa

but seriously

Im not sure if someone mentioned this already but...

0^0/0^0 = 1

the ^0 should cancel out so ((0^0)^1/0)/((0^0)^1/0) = 0/0 = 1

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O = 1... O/O = 1... ta daa

but seriously

Im not sure if someone mentioned this already but...

0^0/0^0 = 1

the ^0 should cancel out so ((0^0)^1/0)/((0^0)^1/0) = 0/0 = 1

I though of that one....but 0^0 is defined as "undefined" so the ans is undefined/undefined

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the sign / can also mean a fraction and if there is the same number on either side of it like a zero on e eaiter side of it or a two on either side of it makes ONE whole so, zero over zero equals one whole, I think

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X = 0

1x/1x = 1

2x/2x = 1

8723x/8723x = 1

all of those times X is 0, though, so:

0/0 = 1

I'm not sure if that was used before as a solution, i didnt look at Page 1 at all

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0 degrees C / 0 degrees C => 273.15 degrees K/ 273.15 degrees K => 1

Don't know when it would meaningful to divide temperatures but...

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There may be another answer, 0dBu/0dBu=1;

u-->unit

because....0dB=10 (or 20) log 1u

so, log1u/log1u=1;

but obviously i makes no sense...when you are talking of x=y=z=.....you should compare in same scale.

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When can the following be true?

0 / 0 = 1

Yes, read as zero divided by zero equals one!

No Tens, unit, magic.. blah blah! guess enuff hint for now

Finally the solution:

dBm is a unit to measure absolute Power, x dBm = 10* log(X^10e+3), where X is power in Watts.

Thus, 1 mw (milli Watt) = 10e-3 W = 10 * log(1) dBm = 0 dBm

Now, 0 (in dBm) / 0 (in dBm) = 1 (but Obvious)

So fellas, spot any fallacies?

Gee, should acknowledge some guy in SD for some funny questions on dBm scale which led to this q. Me thinks it makes cracker of a q

I need some help understanding this one...

What is the claimed obviousness of 0 (in dBm) / 0 (in dBm) = 1?

Decibels are logarithms of power ratios: you take ratios of power values, then take log to get dB values.

Then, you add and subtract dB values to conveniently express multiplicative power gains and losses, respectively.

Which leaves me wondering ...

[1] why are you dividing [instead of subtracting] two decibel numbers

[2] what is the physical significance of ratios of decibel values and

[3] where is the obviousness that attaching units to 0's makes their ratio unity? :huh:

What I do understand is 0[dBm] - 0[dBm] = 0. Meaning the ratio of two 1-mW signals is 1, whose log is 0.

I think someone sold you an interesting story ... B))

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That's sort of what I was thinking . . . that we can just raise it to the power of 0.

(0/0)^0 = 1

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