Mathematicians post a video to youtube twice a year about how 0^0 is debated and controversial but it's literally so simple.The function x^y is always 0 along the x-axis and always 1 along the y-axis.When you zoom in around 0,0 the plotted surface gets increasingly fucked and disjoint, because 0,0 is a singularity. Why do so many people fall for the clickbait?
>>16479730use case?
[math]0^0=1[/math] and anyone who disagrees is a retardthe fact that 0 is your base doesn't matter - it's quite literally the empty product
>>16479842>i dont do anything >i somehow get 1 by not doing anything mathematicians are fucking RETARDED
>>16479747there is none.never in any real world scenario will you need to raise zero to the zeroth power nor will it matter what the "real" answer is. its just mathematicians pontificating about angles on the head of a pin.
>>16479842This, nothing is being multiplied. In the expression x^0, x doesn't participate.
>>16479885Not multiplying a number by anything is the same as multiplying it by 1. If I've got the number 5 and I just don't multiply it by another number, it doesn't suddenly turn into zero.
>>16479930>If I've got the number 5 and I just don't multiply it by another number, it doesn't suddenly turn into zero.ok then explain why it suddenly turns into 1.
>>16479932NTA but 5 doesn't turn into 1, there's no 5. Nothing "turns into" anything
>>16479932It doesn't, rather the absence of multiplication is the same as 1, just like the absence of addition is the same as 0.If I start with nothing and I don't multiply it by anything, that's still nothing because 0×1 is zero. But 0^0 isn't necessarily starting with nothing. You can define the exponentiation to include an implicit 1 without contradicting anything about how it works in any other situation. And then using that definition, 0^0 can be interpreted as 1×0^0, or "What do you get when you take 1 and multiply it by zero zero times? Which of course is still 1.
>>16479940but 1 multiplied by 0 = 0...
>>16479957>1 multiplied by 0 = 0"x mutliplied by 0" means you add x 0 times. Meaning that you don't add anything."x exponentiated by 0" means you multiply x 0 times. Meaning that you don't multiply anything.
>>16479932I start off with 2.I don't multiply it by 5.What do I end up with?
>>16479730>0^0this is just the big bang. why are all of you retarded?
>>16479730>You can't divide by zero! It's undefined, math doesn't allow it!>Black holes have real singularities Makes you think
>>16479730The exponential is only properly defined for something like 0^0 via analytic continuation, ie 0^0 = e^(0*ln0). The RHS is clearly undefined, but its right-sided limit evaluates to 1. So 0^0 is undefined, but lim_a->0^+ a^a= 1.
>>16480492The exponential is only properly defined for something like 0^1 via analytic continuation, ie 0^1 = e^(1*ln0). The RHS is clearly undefined, but its right-sided limit evaluates to 0.So 0^1 is undefined, but lim_a->0^+ a^(1+a)= 0.
>>16479963So if you don't have anything and you don't multiply it by anything, you suddenly have 100% of a thing?
>>16480465No, you are thinking of 0!.
>>16480541if you have 3 and multiply it by nothing you have 3if you have 3 and multiply it by 1 you have 3multiplication by nothing is the same thing as multiplication by 1 qed
>>16480578>multiplication by nothing is the same thing as multiplication by 1 qedNo, nothing is the additive element which is quantized as 0 and 0 multiplied by anything is always 0.Adding nothing is the same thing as multiplying by 1, but not multiplying by nothing, multiplying by nothing is like adding the opposite number.
>>16480578Zero is not the same thing as nothing
I'm following the lead you clue directly at now.
>>16480600see >>16480603"nothing" in the context of an operation means the identity of that operation. You don't delete a square by "doing nothing" to it
>>164806030 is the numerical equivalent of nothing since they are attempts to logically describe an additive identity.
>>16480637You nullify a square by multiplying it by nothing since that is a multiplicative annihilator.
>>16480600>have 3>don't multiply it by anything>suddenly don't have 3explain
>>16480541You don't "suddenly" have anything. The background of multiplication is 1. It's always there. If you don't put anything else on the background, all you have is the same thing you always had, 1.
>>16479730>Scp-1471 is a big tiddy goth wolf temptress. D class and foundation staff alike have commented on it's lustful figure, several attempts were made to solicit intercourse by personnel prior to scp-1471's relocation to site 11 and revision of containment protocols. Relocation was prompted by event 1471-A.Event 1471-A log.This log transcribes events recorded by several CCTV cameras adjacent to and inside scp-1471's cell.Dr ------ can be seen walking down the corridor towards scp-1471's cell, Dr ------ exchanges some words between the single guard on duty, Sgt ----, before passing him a brown envelope. Sgt ---- allows unlocks scp-1471's cell and permits Dr ------ to enter before closing the door behind him resuming his duties. Dr ------ immediately begins to communicate with scp-1471, the conversation suggests Dr ------ used prior authorized interactions with scp-1471 to arrange this meeting. Dr ------ makes several crude remarks on the attractiveness of scp-1471, which plays off these and attempts to ply Dr ------ for security information relevant to egressing the facility. A series of escalations initiated by Dr ------ result in both parties finding themselves in a state of undress. From this point onwards scp-1471's attempts to attain more information become more forceful, with questions overtly specific to methods of escaping the facility raised. Dr ------ and scp-1471 initiate coitous once Dr ------ reveals his access code to Entrance Zone gate.Little of academic relevance is discussed during the following 3 minutes. This end period is marked by Dr ------'s exclamations of increasingly powerful contractions by scp-1471. It is moments after this that a sector wide lockdown is declared after Dr ------'s howls of confused ecstasy and agony are overheard. It is hypothesized that Dr ------'s genitals were obliterated around this time. MTF agents report to scp-1471's cell within 2 minutes, and are able to separate Dr ------ and scp-1471.End log.
>>16480649NTA but if you "have 3" and don't multiply it by anything, you still have 1 copy of 3. That's not 3^0, it's 3^1.
>>16480538This is different because 1*ln0 is -infinity. The usual limit techniques for natural numbers still work. Whereas 0^0 is something that requires L’Hospital’s rule, ie a notion of differentiation. So it’s meaningless to talk about 0^0 in the context of non-differentiable functions.
>>16480677it's [math]3^1 \times x^0[/math] for arbitrary[math]x[/math]
>>16480932Sure, you could describe that post that way, too.What anon seems to be missing is that x is arbitrary for any x^0 because no x is actually involved anywhere in what that operation describes.
>>16480483Black holes don't have real singularities you idiotic pop soience consoomer. They encompass finite volumes with finite mass.
it's definitely 1 but I actually forget why as it's been a long time since high school. But, negative exponents are between 0 and 1, an exponent of 1 is the number, and so an exponent of 0 being 1 makes sense.
>>16479730
>>16479842Bullshit. (You need to be 18+ to post on 4chan. Are you?) [math]x^0=x^{(1-1)}=\frac{x}{x}[/math]. Now, substitute x with zero...
>>16480674>The background of multiplication is 1. It's always there.Then why isn't 0*x=1?>If you don't put anything else on the background,They did, though, they put 0 in the background and the foreground.
>>16480959Are you blind or just being disingenuous? x is set to 0 in the 0^0 operation being described.
my 0^0 identifies as female
If 0/0 = 1 then 0 is a prime number
>>16481906It's set to 0 and, like any other x in the operation x^0, doesn't participate anywhere in what the operation describes.
>>16481904>Then why isn't 0*x=1?Because the background of addition is 0.>they put 0 in the background and the foregroundNo, they put nothing anywhere. x^0 means that no multiplication is happening.
>>16481872It's common for people who fail at latex to also fail at understanding the difference between continuity and single operations.
>>16479963so if you multiply it 0 times doesn't x stay the same? If you multiply 100 dollars 0 times you have $100
>>16482188No addition is in that formula, though, its a product.
>>16482232If you have $100, you've multiplied $100 by 1, not by 0.
>>16482237That's what a product is, it tells you how many copies of something are added.
>>16482246But you said no multiplication is happening if you multiply 0 times, so if there is no multiplication, there is no addition either by that logic.
>>16482260Right, x*0 means no addition is happening. All you ever have is the background 0.
>>16482266That is the opposite of what was said >>16480674
>>16481790Division by zero is undefined for real numbers ,so I don’t think this really proves your point. 0 raised to the zero power seems like a matter of convention. The interpretation of b^0 as an empty product assigns it the value 1.The combinatorial interpretation of b^0 is the number of 0-tuples of elements from a b-element set; there is exactly one 0-tuple.The set-theoretic interpretation of b^0 is the number of functions from the empty set to a b-element set; there is exactly one such function, namely, the empty function.Strikes me as similar to why we define 1 to be not be prime - it screws up things like the fundamental theorem of arithmetic if we don’t.
>>16485981>interpretations of b^0How about interpretation of 0^a? For each a>0 0^a=0 so lim (a->0+) 0^a is also equal to 0.
The definition of exponentiation with a natural number exponent is[eqn]z^n = \begin{cases} 1 & n=0 \\ z \cdot z^{n-1} & n > 0 \end{cases}[/eqn]So [math]0^0 = 1[/math].
>>16486010What if zero is not a natural number?
>>16486011Ex falso quodlibet
a whole thread of pointless pseud shit when you could just have opened your browser console and checked what it is lmao
>>16486020>pseud>lmaoYou've got to get back to /pol/, stray election tourist.
>for any x, 0^x = 0>0^0 = 1 in most programming languagesprogrammers are the pseuds
>>16486101>for any x, 0^x = 0Consider x=-1 or any other non-positive x.
>>16486121yes I have considered that these cases are undefined and experts agree with me
>>16486010[eqn]z^{n} = \left\{ \begin{array}{cl}z & : \ n = 1 \\\frac{z^{n+1}}{z} & : \ n < 1\end{array} \right.[/eqn]
>>16486005The limit existing from the right does not guarantee the function equals the value of the limit. Consider a piece wise function that maps x to x squared if x does not equal 1 and maps x to a billion if x equals 1. Here the limit as x approaches 1 exists and equals 1 ,yet the function itself does not equal 1 at x=1.I reiterate that 0 raised to 0 is defined to be 1 by convention. For example, the power rule of differentiation is only valid for n=1 and x=0 if 0 raised to the zero equals 1.
>>16485968It's the same.For ^0>You don't "suddenly" have anything. The background of multiplication is 1. It's always there. If you don't put anything else on the background, all you have is the same thing you always had, 1.For *0>You don't "suddenly" have anything. The background of addition is 0. It's always there. If you don't put anything else on the background, all you have is the same thing you always had, 0.
