/sci/ - Science & Math » Thread #11653605

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If you believe it's 1, you're a bluepilled faggot

Anonymous Sat 09 May 16:39:21 2020 No.11653605 View Reply Original Report

Quoted By: >>11653613 >>11653618 >>11653639 >>11653660 >>11653689 >>11653697 >>11653725 >>11653853 >>11654186 >>11654719 >>11655363 >>11655365 >>11655774 >>11655776 >>11655816

Anonymous

Anonymous Sat 09 May 2020 16:43:20 No.11653613 Report

Quoted By: >>11653620 >>11653639 >>11653657 >>11653746 >>11653752

>>11653605
It cant be one.
Sure, $\lim_{x \rightarrow 0} x^x = 0$ , but thats just one way to approach 0^0

Anonymous

Anonymous Sat 09 May 2020 16:44:17 No.11653618 Report

Quoted By: >>11653639

>>11653605
That expression hardly makes sense.

Anonymous

Anonymous Sat 09 May 2020 16:44:23 No.11653620 Report

Quoted By: >>11653752

>>11653613
Fuck, i meant $\lim_{x \rightarrow 0} x^x = 1$

Anonymous

Anonymous Sat 09 May 2020 16:51:11 No.11653639 Report

Quoted By: >>11654190

>>11653605
>>11653613
>>11653618
it's undefined, so one can define it to be whatever they want

Anonymous

Anonymous Sat 09 May 2020 16:58:03 No.11653657 Report

Quoted By:

>>11653613
Yeah, but your approaching it with number greater than zero.

Zero should not be considered a real number. It exists in all dimensions

Anonymous

Anonymous Sat 09 May 2020 16:58:43 No.11653660 Report

Quoted By:

>>11653605
its 1

Anonymous

Anonymous Sat 09 May 2020 17:08:14 No.11653689 Report

Quoted By:

>>11653605
You do not `believe' it is 1. Instead you use the definition of exponentiation, which explicitly tells you that it is 1.

Anonymous

Anonymous Sat 09 May 2020 17:12:14 No.11653697 Report

Quoted By: >>11653714

>>11653605
it's infnininty

Anonymous

Anonymous Sat 09 May 2020 17:19:05 No.11653714 Report

Quoted By:

>>11653697
Infinity isn't a number

Anonymous

Anonymous Sat 09 May 2020 17:22:22 No.11653725 Report

Quoted By:

>>11653605
Anything raised to the zeroth power is the empty product. The empty product must be equal to one, for indexed products with bounds that produce zero elements to evaluate properly, i.e.:

$\prod_{i=1}^0 a_i = 1$

Anonymous

Anonymous Sat 09 May 2020 17:29:00 No.11653746 Report

Quoted By: >>11653774

>>11653613
That limit is only true from the right side.

Anonymous

Anonymous Sat 09 May 2020 17:33:03 No.11653752 Report

Quoted By:

>>11653613
>>11653620

Can the limit be with any function or pair of functions?

Be: $u(x) = -{1 \over ln(x)}$

$lim_{x \to 0} u(x) = 0$

$lim_{x \to 0} u(x)^{u(x)} \nexists? 1?$

$lim_{x \to 0} x^{u(x)} = e^{-1}$
$lim_{x^ \to 0} (x^\alpha)^{u(x)} = e^{-\alpha}$
$lim_{x^ \to 0} (\alpha x)^{u(x)} = e^{-1}$

$(\alpha x)^u$ converges to $e^{-1}$ "very slowly"

Anonymous

Anonymous Sat 09 May 2020 17:40:34 No.11653774 Report

Quoted By:

>>11653746
It's also true for the left side limit.
If x is a real negative number then

x^x = e^(x log(|x|)) cos(pi x) + i e^(x log(|x|)) sin(pi x)
Now if you let x -> 0 then
e^(x log(|x|)) -> 1
cos(pi x) -> 1
sin (pi x) -> 0
So
x^x -> 1

Anonymous

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Anonymous Sat 09 May 2020 17:46:15 No.11653789 Report

Quoted By: >>11653803 >>11654288 >>11654306

You get a number greater than zero by multiplying zero by itself zero times.

Anonymous

Anonymous Sat 09 May 2020 17:52:45 No.11653803 Report

Quoted By: >>11653831 >>11653839

>>11653789
https://www.google.com/search?q=y%3Dx%5Ex&oq=y%3Dx%5Ex

Anonymous

Anonymous Sat 09 May 2020 18:04:23 No.11653831 Report

Quoted By:

>>11653803
https://www.google.com/search?hl=en&source=hp&ei=iPC2XsKhLpCKtQXZ6IPoDA&q=y%3D0%5Ex&oq=y%3D0%5Ex&gs_lcp=CgZwc3ktYWIQAzICCAAyBAgAEB4yBAgAEB4yBAgAEB4yBAgAEB4yBAgAEB4yBggAEAUQHjIGCAAQBRAeMgYIABAFEB4yBggAEAUQHjoFCAAQgwFQrQtYryRg5SdoAHAAeACAAbUDiAHqBZIBBTQuNC0xmAEAoAEBqgEHZ3dzLXdpeg&sclient=psy-ab&ved=0ahUKEwjChYv-rqfpAhUQRa0KHVn0AM0Q4dUDCAk&uact=5

Anonymous

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Anonymous Sat 09 May 2020 18:09:33 No.11653839 Report

Quoted By: >>11654193 >>11654202

>>11653803

Anonymous

Anonymous Sat 09 May 2020 18:15:57 No.11653853 Report

Quoted By: >>11653867

>>11653605
Reminder, math is just a framework to explore reality and logic, and isn't actually real

Anonymous

Anonymous Sat 09 May 2020 18:22:10 No.11653867 Report

Quoted By: >>11654162

>>11653853
Semantic arguments based around the definition of "real" or "exists" are only relevant to descriptions of reality, not reality itself. Mathematics are some intangible part of reality, though.

Anonymous

Anonymous Sat 09 May 2020 20:12:46 No.11654162 Report

Quoted By: >>11654417

>>11653867
>entirely depends on how we define the symbols 0, 1, and exponential operations
>literally a stupid thing to argue about
>question has no logical basis in describing reality
>yfw you are the one making the semantic arguments

Anonymous

Anonymous Sat 09 May 2020 20:20:00 No.11654186 Report

Quoted By: >>11654619

>>11653605
It’s 1.
See https://math.stackexchange.com/questions/11150/zero-to-the-zero-power-is-00-1.

Anonymous

Anonymous Sat 09 May 2020 20:21:01 No.11654190 Report

Quoted By: >>11655881

>>11653639
>it's undefined
Wrong.

Anonymous

Anonymous Sat 09 May 2020 20:22:02 No.11654193 Report

Quoted By: >>11654202

>>11653839
The limit doesn’t exist for 0^x, so it doesn’t matter. It gets btfo by x^0.

Anonymous

Anonymous Sat 09 May 2020 20:26:41 No.11654202 Report

Quoted By:

>>11653839
>>11654193
Furthermore, in the Riemann sphere,
$0^s = \begin{cases} 0 & \operatorname{Re} s > 0 \\ \infty & \operatorname{Re} s < 0 \end{cases}$
So it’s unsurprising that $0^0=1$ since 1 is a sort of “geometric mean” between 0 and $\infty$ .

Anonymous

Anonymous Sat 09 May 2020 20:57:16 No.11654288 Report

Quoted By:

>>11653789
>imagine not understanding shit about mathematics

Anonymous

Anonymous Sat 09 May 2020 21:04:44 No.11654306 Report

Quoted By: >>11655702

>>11653789
Correct.
Did you know you get a number greater than 1/2 by multiplying 1/2 by itself 1/2 times?

Anonymous

Anonymous Sat 09 May 2020 21:43:24 No.11654417 Report

Quoted By: >>11654597 >>11654607

>>11654162
Definitions don't matter. The "existence" of mathematical structures is independent of their symbolic description.

Anonymous

Anonymous Sat 09 May 2020 22:47:20 No.11654597 Report

Quoted By: >>11654616 >>11654643

>>11654417
One could presumably design a system of math where 0^0 was something other than 1, depending on their definitions of the exponent operation, and still have it be logically consistent. The fact we defined it as such because it conveniently fits into our mathematical trends does not uncover some deep fundamental truth. It literally just say that that’s how it is in our system of math, which I don’t find elegant or interesting in the slightest. There is nothing fundamental this conversation is elucidating other than how we formalized it

Anonymous

Anonymous Sat 09 May 2020 22:50:47 No.11654607 Report

Quoted By: >>11654619

>>11654417
One more thing. I do believe in deep fundamental mathematical truths like pi and e, which explains a lot of fundamental interactions seen all over in math . But the topic of this thread is not fundamental or interesting imo

Anonymous

Anonymous Sat 09 May 2020 22:54:38 No.11654616 Report

Quoted By:

>>11654597
>does not uncover some deep fundamental truth
Yes it does.

Anonymous

Anonymous Sat 09 May 2020 22:55:40 No.11654619 Report

Quoted By:

>>11654607
It *is* interesting for several reasons. See >>11654186

Anonymous

Anonymous Sat 09 May 2020 23:02:57 No.11654643 Report

Quoted By: >>11654668 >>11654673

>>11654597
You can define x^y to be anything, there is no God given decree that it has to have anything to do with "exponentiation". Why not define x^y := (x+y)/2, the average of x and y? It is much easier to understand, the brainlets will be happy. In all secrecy, you could invent another notation, something like x%y for actual exponentiation. Since brainlets would not know about this development, they are still happy. Profit.

Anonymous

Anonymous Sat 09 May 2020 23:14:23 No.11654668 Report

Quoted By: >>11654674 >>11654681 >>11654694

>>11654643
There are things in math that are clearly true just from logic, and others that are arbitrarily chosen because it is useful for simplified our equations or theories on numbers. For example, the identities for exponents are pretty fundamental. You could write it differently but the math underneath can’t logically be changed. However, 0^0 definition is chosen completely out of convenience

Anonymous

Anonymous Sat 09 May 2020 23:15:41 No.11654673 Report

Quoted By:

>>11654643
I wasn’t talking about the meanings of the symbols with. Of course you could represent stuff with different symbols

Anonymous

Anonymous Sat 09 May 2020 23:16:03 No.11654674 Report

Quoted By:

>>11654668
It's not mere convenience. It IS equal to one.

Anonymous

Anonymous Sat 09 May 2020 23:21:01 No.11654681 Report

Quoted By:

>>11654668
>0^0 definition is chosen completely out of convenience
wrong, it's equal to 1 because it's an empty product

Anonymous

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Anonymous Sat 09 May 2020 23:23:41 No.11654691 Report

Quoted By: >>11654704 >>11654713 >>11655909

Consider the statement
$0 \neq 1$
Raise both sides to the power 0, then we get
$0^0 \neq 1$

Anonymous

Anonymous Sat 09 May 2020 23:25:45 No.11654694 Report

Quoted By:

>>11654668
>0^0 definition is chosen completely out of convenience
Although in some ways you do not have much choice. For sets X and Y you write the set of functions from Y to X in the notation X^Y. Then if X has x elements and Y has y elements, you write the number of such functions as |X^Y| = |X|^|Y| = x^y. Once you make that convention, you are forced to 0^0 = 1, since there is exactly one function (the empty function) from the empty set to itself.

Anonymous

Anonymous Sat 09 May 2020 23:28:29 No.11654704 Report

Quoted By:

>>11654691
Funny picture

Anonymous

Anonymous Sat 09 May 2020 23:28:58 No.11654705 Report

Quoted By: >>11654733

n^p = how many ways are there to arrange a p-list of n elements ?

so

0^0 = how many ways are there to arrange a list (of length 0) consisting of 0 elements (which is logical since its of length 0)

Anonymous

Anonymous Sat 09 May 2020 23:30:58 No.11654713 Report

Quoted By: >>11654782 >>11655112

>>11654691
Consider the statement
$-1 \neq 1$
Raise both sides to the power 2, then we get
$(-1)^2 \neq 1^2$

Anonymous

Anonymous Sat 09 May 2020 23:33:26 No.11654719 Report

Quoted By:

>>11653605
Sir, this is actually against the rules of /sci/, I'll have to report your post for doing vulgar operations with zero.

Anonymous

Anonymous Sat 09 May 2020 23:41:00 No.11654733 Report

Quoted By: >>11654738

>>11654705
Combinatorially, you are asking for the number of ways to assign to each entry of a list of length p an element of a set of size n. In general this is the same as the number of functions from a set of p elements to a set of n elements, since of the p entries can be assigned any one of the n possible contents. From the fact that the number of functions from the empty set to the empty set is 1, i.e. there is exactly one list that is completely empty, we have 0^0 = 1.

Anonymous

Anonymous Sat 09 May 2020 23:43:19 No.11654738 Report

Quoted By:

>>11654733
thats indeed what i was trying to say, there is only one way to arrange the empty set

Anonymous

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Anonymous Sun 10 May 2020 00:00:18 No.11654782 Report

Quoted By: >>11654792

>>11654713
Fine. Consider the statement
$0^0 = 1$
Take the zeroth root of each side to get
$0 = 1$
A contradiction.

Anonymous

Anonymous Sun 10 May 2020 00:04:32 No.11654792 Report

Quoted By: >>11654812

>>11654782
Consider the statement.
$(-1)^2 = 1^2$
Take the second root of each side to get
$-1 = 1$
A contradiction.

Anonymous

Anonymous Sun 10 May 2020 00:14:40 No.11654812 Report

Quoted By: >>11655102

>>11654792
that's wrong because
$(1^2)^(1/2) = \pm 1$

Anonymous

Anonymous Sun 10 May 2020 02:11:03 No.11655102 Report

Quoted By: >>11655323 >>11655326

>>11654812
And the zeroth root isn't unique either. Literally every number raised to the zeroth power is 1.
0^0 = 1^0 = 2^0 = 3^0 = ...
does not imply 0 = 1 = 2 = 3 = ...

Anonymous

Anonymous Sun 10 May 2020 02:17:32 No.11655112 Report

Quoted By: >>11655332

>>11654713

0 is not negative buddy but nice try

Anonymous

Anonymous Sun 10 May 2020 04:05:25 No.11655323 Report

Quoted By: >>11655326

>>11655102
I live in $\mathbb{Z}$ tho

Anonymous

Anonymous Sun 10 May 2020 04:06:28 No.11655326 Report

Quoted By:

>>11655323
>>11655102

correction $\mathbb{Z}/\mathbb{Z}$

Anonymous

Anonymous Sun 10 May 2020 04:09:39 No.11655332 Report

Quoted By:

>>11655112
>I'm going to make an irrelevant post
ok

Anonymous

Anonymous Sun 10 May 2020 04:26:08 No.11655363 Report

Quoted By:

>>11653605
Its just undefined because 0^0 = 0/0

Anonymous

Anonymous Sun 10 May 2020 04:29:10 No.11655365 Report

Quoted By: >>11655368

>>11653605
The HOLY CRUSADE against the HERETICS continues! Praise GOD!

Listen up, SINNERS, zero does NOT exist! Therefore attempting to raise zero to the power of zero is a double AFFRONT to the ALMIGHTY!

Any attempt to do will result in you being cast straight down into the finite fires of HELL!!

OP is granted a dispensation because he is attempting to turn you GODLESS SODOMITES away from SIN and back into the loving BOSOM of GOD!

Anonymous

Anonymous Sun 10 May 2020 04:31:35 No.11655368 Report

Quoted By:

>>11655365
Haha based! I tip my fedora to you

Anonymous

Anonymous Sun 10 May 2020 05:09:21 No.11655446 Report

Quoted By: >>11655473

math is all by definition. In some cases it's useful to have 0^0 = 1 and in some it's useful to have 0^0 = 0. It can be whatever we want

Anonymous

Anonymous Sun 10 May 2020 05:18:47 No.11655473 Report

Quoted By:

>>11655446
Brainlet take

Anonymous

Anonymous Sun 10 May 2020 08:06:17 No.11655702 Report

Quoted By:

>>11654306
Wtf. It's true. I don't think I ever thought about it that way.

Anonymous

Anonymous Sun 10 May 2020 08:49:08 No.11655774 Report

Quoted By: >>11655792

>>11653605
Does this mean that the universe was created when nothing squared itself....

Anonymous

Anonymous Sun 10 May 2020 08:50:53 No.11655776 Report

Quoted By: >>11655794

>>11653605

0 is a lack of existence. Zero. If you multiply 0 to the power of zero you're just multiplying nothing by nothing.

Anonymous

Anonymous Sun 10 May 2020 08:59:21 No.11655792 Report

Quoted By:

>>11655774
square is 2nd power not 0th but yeah pretty much. the total energy of the universe is 0

Anonymous

Anonymous Sun 10 May 2020 09:00:30 No.11655794 Report

Quoted By: >>11655796

>>11655776
Then what's 10^0? Multiplying 10 with nothing so you get nothing? But the result is 1.

Anonymous

Anonymous Sun 10 May 2020 09:05:16 No.11655796 Report

Quoted By:

>>11655794

I forgot that powers inherently are predicated by 1 so even a 0 power is technically 1, but 00 is still 1 multiplied by 0. It's just theoretical math autism to make equations work.

Anonymous

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Anonymous Sun 10 May 2020 09:27:01 No.11655816 Report

Quoted By:

>>11653605

Anonymous

Anonymous Sun 10 May 2020 10:20:06 No.11655881 Report

Quoted By:

>>11654190
source: my ass

Anonymous

Anonymous Sun 10 May 2020 10:46:46 No.11655909 Report

Quoted By:

>>11654691
consider the statement
$0.999... \neq 1$
multiply both sides by 0, then we get
$0 \neq 0$
clearly a contradiction, therefore $0.999... = 1$

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