What is (1/0)^0?

What is (1/0)^0?

= 1^0 / 0^0
= 1 / undefined
undefined

Which field are we working in?
Since in [math](\mathbb{R}, +, \times)[/math] 0 has no inverse.

why does it have to be a field? why not a ring?

also why is it called a field? because fields extend out infinitely in the landscape sense?

Right answer, incorrect steps. See order of operation.

=(1/0)^0
=(undefined)^0
=undefined

0^0 = 1

0^0 is undefined

By definition a field is a commutative division ring. We could work in a ring like you said, but we don't guarantee commutativity, in which case writing [math]\frac{1}{0}[/math] is ambiguous since it could mean either [math]10^{-1}[/math] or [math]0^{-1}1[/math].
For the nomenclature, I don't know.

0^0 is undefined formally and =1 at best.
You'd have to show a proper proof because as of right now that's also wrong.

Both false. These also show that every number is equal to every other number.

>implying they aren't

>see order of operation
gb2/ 8th grade

(a/b)^n = (a^n)/(b^n) fucking retard

Let's fall for the le transcendental continuation meme.
[eqn]\left( \frac{1}{x} \right)^x \,=\, \mathrm e^{x\,\ln\,\frac{1}{x}} \,=\, \mathrm e^{-x\,\ln\,x}[/eqn]
Since [math]x\,\ln\,x \,\xrightarrow[x \,\rightarrow\, 0]{}\, 0[/math], we have [math]\lim_{x \,\rightarrow\, 0} \left( \frac{1}{x} \right)^x \,=\, \mathrm e^0 \,=\, 1[/math].

>not taking L'Hospitals rule

Sorry, you're absolutely right in that we cannot assume that they aren't since we have yet to establish So as it stands, this question is missing context or other details.

Lame.
I'll invent a number! It will be indivisible by every number! It won't even be divisible by 1 .! And it will have all signs at once! It'll be negative, positive, imaginary... everything! And its value won't even make sense!

Would that have any practical purpose?

In the case where the derivative is not defined, and thereby L'Hospitals rule won't yield any usable forms, does Squeeze theorem always apply?

>won't work because 1^0 will make it not indeterminate

What about sinx/x , x=0 ?
L'Hospitals rule yields cosx/1
literally 1/1 = 1

No... Not until some-one finds a use for it anyway.

Don't trust them. They couldn't even do a simple fraction question last year. Not even joking. /b/, on average scored higher than Veeky Forums. Disappointment. But /b/ were more willing to learn and understand their mistakes. But Veeky Forums held back from that a bit

The limit of a constant is a constant.
1^0 is a constant
sin x is a function

Let P be a point in the center of my anus.

If I insert a dildo into my anus at P that widens .3 inches in radius with every inch in length, what is the rate at which my anus widens while inserting the 30th inch of dildo?

How quickly are you pushing and is it accelerating, do we take into account rectal prolapse

constant velocity of +4cm/sec

limit of sin(x/x) x-->0 isn't the same as sin(0/0).

>using inches on a science board
BTFO imperial brainlet

American Engineers use imperial. Especially ChemE, huge amounts of stuff are commonly measured in a unit called lb-mol.

>American Engineers
wew lad

My calculator says Not a Number. What's giraffe squared=?

I have the only decent calculator in the world and it says 1 with a warning: "undef^0 was replaced with 1". What is your excuse for not getting this?