/sci/ - Science & Math » Thread #12462727

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Anonymous Mon 14 Dec 03:42:12 2020 No.12462727 View Reply Original Report

Quoted By: >>12462734 >>12462738 >>12462790 >>12463085 >>12463168 >>12463188 >>12463249 >>12463353 >>12463460 >>12464101 >>12464126 >>12465582 >>12465648

Alright /sci/, here's an easy one so don't over think it.

0^0=?

Anonymous

Anonymous Mon 14 Dec 2020 03:42:53 No.12462729 Report

Quoted By:

fuck you

Anonymous

Anonymous Mon 14 Dec 2020 03:43:39 No.12462734 Report

Quoted By: >>12462796 >>12463052

>>12462727
1. The number of functions from the empty set to itself is one: the empty function.

Anonymous

Anonymous Mon 14 Dec 2020 03:45:10 No.12462738 Report

Quoted By: >>12463359

>>12462727
undefined

Anonymous

Anonymous Mon 14 Dec 2020 03:53:53 No.12462756 Report

Quoted By: >>12462760 >>12462764

notational abuse.
show me the arithmetic algorithm that describes this process.

Anonymous

Anonymous Mon 14 Dec 2020 03:55:05 No.12462760 Report

Quoted By: >>12462849 >>12463359

>>12462756
easy. 0/0

Anonymous

Anonymous Mon 14 Dec 2020 03:56:38 No.12462764 Report

Quoted By: >>12462849 >>12463359

>>12462756
x^x as x approaches 0

Anonymous

Anonymous Mon 14 Dec 2020 04:08:53 No.12462790 Report

Quoted By:

>>12462727
>easy, one

Anonymous

Anonymous Mon 14 Dec 2020 04:13:30 No.12462796 Report

Quoted By:

>>12462734
this

Anonymous

Anonymous Mon 14 Dec 2020 04:32:06 No.12462833 Report

Quoted By: >>12463359

Let $\ell\,\in\,\mathbf C$ . For all $x\,\in\,\mathbf R$ , we have
$x^{x\,\ln\,\ell} \;=\; \mathrm e^{x\,\ln\,\ell\,\ln\,x}.$
Taking the limit as $x\,\to\,0$ , we get
$0^0 \;=\; \mathrm e^{\ln\,\ell} \;=\; \ell.$
Therefore, $\forall\ell\,\in\,\mathbf C,\,0^0\;=\;\ell$ .

Anonymous

Anonymous Mon 14 Dec 2020 04:37:52 No.12462849 Report

Quoted By:

>>12462764
x^x is another notion.
what algorithm represents with notation?
>>12462760
0/0 is 0*h = 1.

Anonymous

Anonymous Mon 14 Dec 2020 06:16:36 No.12463052 Report

Quoted By: >>12463477

>>12462734
how many functions are there from a set with cardinality pi to itself? I need to know what pi^pi is.

Anonymous

Anonymous Mon 14 Dec 2020 06:35:55 No.12463085 Report

Quoted By:

>>12462727
if you want to keep the property of the a^x function (a is in this case 0) that it is a homorphism from the additive group to multiplicative group, it has to be 1, because the value of the neutral element is the neutral element of the other group.
if you want to define a^x as exp(ln(a)*ln(x)) a can't be zero

Anonymous

Anonymous Mon 14 Dec 2020 07:14:23 No.12463168 Report

Quoted By:

>>12462727
0, you multiply 0 * 0

Anonymous

Anonymous Mon 14 Dec 2020 07:26:39 No.12463188 Report

Quoted By:

>>12462727
$0^{\pm\infty}$ is the only additive identity in the extended complex plane
$0^1$ is not the additive identity, since $0^1 * \frac{1}{0^1}=1$ . Likewise with $0^2 * (\frac{1}{0^2})=1$ ; $0^3 * (\frac{1}{0^3})=1$ , etc.
So for $0^0$ :
$0^0 * (\frac{1}{0^0}) = 0^0 * (\pm\infty)^0 = 0^0 * 1 = 1$
therefore $0^0=1$

Anonymous

Anonymous Mon 14 Dec 2020 07:54:34 No.12463249 Report

Quoted By:

>>12462727

Anonymous

Anonymous Mon 14 Dec 2020 08:56:44 No.12463353 Report

Quoted By: >>12463466

>>12462727
Its 1 you fucking retards you lean that in highschool, a^0=1, a CAN = 0

Anonymous

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Anonymous Mon 14 Dec 2020 08:57:47 No.12463359 Report

Quoted By:

>>12462738
>>12462760
>>12462764
>>12462833

Anonymous

Anonymous Mon 14 Dec 2020 10:01:46 No.12463460 Report

Quoted By: >>12463852

>>12462727
0!

Anonymous

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Anonymous Mon 14 Dec 2020 10:02:52 No.12463465 Report

Quoted By:

Anonymous

Anonymous Mon 14 Dec 2020 10:03:04 No.12463466 Report

Quoted By: >>12463868

>>12463353
My high school taught calculus and limits and led me to believe 0^0 is indeterminate.

Anonymous

Anonymous Mon 14 Dec 2020 10:10:10 No.12463477 Report

Quoted By: >>12463510

>>12463052
>pi
Not a number.

Anonymous

Anonymous Mon 14 Dec 2020 10:11:09 No.12463478 Report

Quoted By: >>12465683

$0^0$
$=e^{0 \log{0}}$
$=\lim_{x\to0} xlog(x)$
$0 \times \infty$
Indeterminate form

Anonymous

Anonymous Mon 14 Dec 2020 10:19:38 No.12463510 Report

Quoted By: >>12463875

>>12463477
https://en.wikipedia.org/wiki/Pi
>The number ? is a mathematical constant.
>Being an irrational number, ? cannot be expressed as a common fraction.
>It is known that ? is a transcendental number

Anonymous

Anonymous Mon 14 Dec 2020 12:09:52 No.12463852 Report

Quoted By: >>12463865

>>12463460
1!

Anonymous

Anonymous Mon 14 Dec 2020 12:12:29 No.12463865 Report

Quoted By:

>>12463852
.9...

Anonymous

Anonymous Mon 14 Dec 2020 12:12:48 No.12463868 Report

Quoted By: >>12463891

>>12463466
You mean made you believe in calculus. I doubt anyone teaches derivations for basic limits. they just pass it on as formulas. lol What a shit show Calculus is

Anonymous

Anonymous Mon 14 Dec 2020 12:15:17 No.12463875 Report

Quoted By: >>12463886

>>12463510
Wikipedia is wrong. If you actually look at their given "definition" you will see that it's actually meaningless.

Anonymous

Anonymous Mon 14 Dec 2020 12:17:12 No.12463886 Report

Quoted By: >>12464442

>>12463875
Which "definition" and how is it wrong and if it is meaningless how did you come to discover its meaning was wrong?

Anonymous

Anonymous Mon 14 Dec 2020 12:18:20 No.12463891 Report

Quoted By:

>>12463868
>You mean made you believe in calculus.
Yes that is a perfectly acceptable synonym for taught, thank you for your super valuable semantic input.

Anonymous

Anonymous Mon 14 Dec 2020 13:53:26 No.12464101 Report

Quoted By: >>12465438

>>12462727
go away

Anonymous

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Anonymous Mon 14 Dec 2020 14:02:41 No.12464126 Report

Quoted By:

>>12462727
0

Anonymous

Anonymous Mon 14 Dec 2020 16:21:24 No.12464442 Report

Quoted By: >>12465527

>>12463886
>Which "definition" and how is it wrong
All of them that I know of. In particular, the Cauchy definition, the Dedekind definition and the almost homomorphism definition and the various variations of thereof.
If you have a definition of the real numbers that you think makes sense, please feel free to present it.
>how did you come to discover its meaning was wrong?
By contemplation together with listening to the arguments by Wildberger, Nelson, Zeilberger and other thoughtful mathematicians.

Anonymous

Anonymous Mon 14 Dec 2020 21:24:28 No.12465438 Report

Quoted By:

>>12464101
bump

Anonymous

Anonymous Mon 14 Dec 2020 21:25:48 No.12465452 Report

Quoted By:

sure. 0 to the power of 0 is 0 times 0. Anything times 0 is always 0.
So the answer is 0.
Pretty fucking easy.

Anonymous

Anonymous Mon 14 Dec 2020 21:37:07 No.12465507 Report

Quoted By:

0^0 := ur mom faggot

Anonymous

Anonymous Mon 14 Dec 2020 21:40:33 No.12465527 Report

Quoted By: >>12465651

>>12464442
You can find the real numbers embedded in the surreal numbers you pretentious faggot

Anonymous

Anonymous Mon 14 Dec 2020 21:55:32 No.12465582 Report

Quoted By: >>12465589

>>12462727
2^2 = 2 * 2 = 4
1^1 = 1 * 1 = 1
0^0 = 0 * 0 = 0
anything else is masturbatory nonsense

Anonymous

Anonymous Mon 14 Dec 2020 21:58:32 No.12465589 Report

Quoted By:

>>12465582
>implying there's a pattern

Anonymous

Anonymous Mon 14 Dec 2020 22:16:30 No.12465648 Report

Quoted By:

>>12462727
I'll do you one better: what's 0^-1?

Anonymous

Anonymous Mon 14 Dec 2020 22:17:30 No.12465651 Report

Quoted By:

>>12465527
>surreal numbers
Doesn't exist.

Anonymous

Anonymous Mon 14 Dec 2020 22:26:31 No.12465683 Report

Quoted By:

>>12463478
x log(x) is actually 0 when x-->0

Anonymous

Anonymous Mon 14 Dec 2020 22:36:44 No.12465739 Report

Quoted By:

>0 multiplied by 0 0 times
that would be empty set

Anonymous

Anonymous Mon 14 Dec 2020 22:41:02 No.12465757 Report

Quoted By:

that would be empty set

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