/sci/ - Science & Math

[Anonymous No.11697980]

>0^0 = 1
math cucks will defend this

[Anonymous No.11697988]

>>11697980
Point and laugh everyone.

[Anonymous No.11697990]

>>11697980
X^0=1

[Anonymous No.11697991]

the identity function exists, even for the empty set

[Anonymous No.11697993]

>>11697980
>reeeee this a fundamental property of exponents reeeee
>muh maths need to follow logical trends even if the result is a completely illogical solution reeeee

[Anonymous No.11698000]

let this be a lesson to you frog poster. intuition is often false

[Anonymous No.11698016]

0^0 is a question of convenience, and it turns out it's most conveient to define as 1.

[Anonymous No.11698024]

>>11698016
Agreed. In any physical context, 0^0 would mean the system is completely stationary, which is not physically interesting.

[Anonymous No.11698030]

>>11697990
prove it

[Anonymous No.11698034]

>>11697980
[math]0^0=1[/math]
https://math.stackexchange.com/questions/11150/zero-to-the-zero-power-is-00-1

[Anonymous No.11698037]

>>11698030
By definition it's the number of functions from the empty set to X. There is one such function, the empty function.

[Anonymous No.11698043]

>>11697980
>>11698030
0^0 ≡ 1

Happy now anon?

[Anonymous No.11698045]

>>11698037
>by definition

by definition ur retarded and gay. wow this math stuff is easy

[Anonymous No.11698052]

>>11698045
Everything in math is defined in terms of more primitive concepts, down to some basic axioms we agree to use. If you have a problem with that I suggest you learn more math or just give it up.

[Anonymous No.11698058]

>>11698052
Its difficult to argue with apes, anon.

[Anonymous No.11698100]

>>11698052
Well we all agree ur retarded and gay. Damn axioms are fun. And intuitively it works because it reflects reality. If you have a problem with that, i guess you can stop being gay.

[Anonymous No.11698196]

>>11698034
Wouldnt it be negative one?

[Anonymous No.11698202]

>>11698196
No.

[Anonymous No.11698218]

>>11697990
0^X=0

[Anonymous No.11698232]

>>11697980
the real question is what the zeroth root of 0 is... 0^(1/0)???

[Anonymous No.11698300]

>>11698232
that would imply division by zero

[Anonymous No.11698414]

It's undefined, you can make it be whatever you want it to be:
[math]g(x) \equiv \frac{c}{\ln x}[/math]
[math]lim_{x\rightarrow 0}\,\,g(x) = 0[/math]
[math]lim_{x\rightarrow 0}\,\,x^{g(x)} = e^c\neq 1 [/math]

[Anonymous No.11698417]

>>11698043
based

[Anonymous No.11698521]

>>11698043
Technically is will always go to be .9 , but muh rounding makes it 1 even though it's factually 9∞. Mentally retarded monkey's can't count that high.

[Anonymous No.11698534]

>>11698030
X^a / X^a =X^a-a=X^0=1

[Anonymous No.11698552]

>>11697980
No, they won't. There is no correct answer to what 0^0 should be.

[Anonymous No.11698553]

>>11698534
and since 0/0 != 1 then 0^0 != 1
everyone else in this thread is a faggot

[Anonymous No.11698554]

>>11698414
This just says (x,y)\mapsto x^y is not continuous at (0,0).

[Anonymous No.11698559]

>>11698554
It is continuous. It equals e^c for all x. The point is 0^0 is an undefined expression much like 0/0 is

[Anonymous No.11698566]

>>11698534
Where X^a cannot be zero since you cannot divide by 0, therefore X cannot be 0

[Anonymous No.11698567]

>>11698554
Oh I misread your point. Yes x^y is not continuous at (x,y)=(0,0). That's another way to see it is undefined

[Anonymous No.11698584]

>>11698566
yeah see >>11698553

[Anonymous No.11698629]

>>11698218
Wrong.

[Anonymous No.11698637]

>>11698553
>0^(n+1) / 0 is division by zero therefore 0^n doesn’t exist
Retard

[Anonymous No.11698642]

>>11698559
It’s not continuous you fucking idiot, it’s not even defined for exponents less than zero, and is infinity for exponents less than zero in the context of the Riemann sphere.

[Anonymous No.11698646]

>>11698566
>>11698584
see >>11698637

[Anonymous No.11698653]

>>11698567
>That's another way to see it is undefined
Wrong, you stupid orangutan. Just because a function is discontinuous at a point doesn’t mean it’s undefined at that point. There are even functions that are discontinuous everywhere.

[Anonymous No.11698656]

>>11698642
It's continuous in x, jackass. Or it has a removable discontinuity at x=0 if you want to be pedantic. Take a little time to understand a post first and you won't seem as stupid

[Anonymous No.11698660]

>>11698653
It absolutely means it's undefined. There is no unique limit. Again, learn a little humility dipshit

[Anonymous No.11698663]

>>11697980
> x^x
> l'hopital
> what is a limit
the absolute state of this board lmao

[Anonymous No.11698664]

>>11698660
YOU'RE A FUCKING IDIOT KILL YOURSELF
https://en.wikipedia.org/wiki/Nowhere_continuous_function

[Anonymous No.11698673]

>>11698660
based retard

[Anonymous No.11698677]

>>11698664
Look, you thinking I have never heard of the idea of a nowhere continuous function like it's some secret knowledge just shows what a middlebrow pleb you are. Step back, learn a little more math, and realize there are people that are as smart or smarter than you, and then come back here

[Anonymous No.11698678]

>>11698656
A multivariate function is said to be continuous when it's simultaneously continuous in all its arguments, dummy. Of course it's continuous in x alone (if you let 0^0 = 1), no shit.

[Anonymous No.11698680]

>>11698677
I'm not the TOTAL RETARD claiming discontinuous means undefined.

But I gracefully accept your concession.

[Anonymous No.11698681]

>>11698678
I'm talking about x in my function g(x). I was agreeing with you

[Anonymous No.11698686]

>>11698554
too big-brain for these idiots

[Anonymous No.11698701]

>>11697980
wtf I hate math now!

[Anonymous No.11698718]

>>11697980
Just from reading up on this briefly, you CAN make 0^0 anything you want, which really means it's undefined, BUT making it equal 1 has an extra way of making it right (how many ways can you make no choices from no things equals one), so it's less wrong than the others.
So 0^0 is undefined, except some times when it's one.

[Anonymous No.11699113]

>>11698718
why on earth would 0^0 be anything other than 1?

[Anonymous No.11699702]

>>11699113
I saw a proof that if you approach the x^y function from a particular direction you can see 0^0 taking any value you want.

[Anonymous No.11699725]

How many times does 0 fit into 0?
One
There you go

[Anonymous No.11699749]

>>11699725
What if I answer two