Mathematical Question || The Zero Root

[Healbadbad]

He's right. You're dividing by zero there.
Sqrt(x) = x^1/2
that's the second root.
0th root = X^1/0

D:


The limit x^1/n as n-> 0  is equal to infinity though.

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[Dropshock]

How do I numbers?

[Gamefandan]

x⁰ = x/1*1/x = x/x = 1

Not hard.

He's right. You're dividing by zero there.
Sqrt(x) = x^1/2
that's the second root.
0th root = X^1/0

D:


The limit x^1/n as n-> 0  is equal to infinity though.

You're thinking it wrong.

[ChexGuy331]

I just don't see how x⁰ = x/x

If x=2, then 2⁰ is equal to 2/2 because 2⁰=1.

I already said that. I learned this in 7^th grade. Some people learned it earlier.

[Daedalus]

If x=2, then 2⁰ is equal to 2/2 because 2⁰=1.

I already said that. I learned this in 7^th grade. Some people learned it earlier.

I know, I know, I've been taught that anything to the zero power is 1, but it just doesn't make sense to me.

I always thought that anything to the zero power equals zero.
My logic is as follows:
2 squared = 2*2 (there are two instances of 2 in the equation)
2 to the zero power = [blank] (there are no 2s)

[Newt24]

I always thought that anything to the zero power equals zero.
My logic is as follows:
2 squared = 2*2 (there are two instances of 2 in the equation)
2 to the zero power = [blank] (there are no 2s)

Technically that is not correct, as you can't just have nothing.

Take this...

3/3 = 1

Now, according to your logic, the answer is 0, because the threes cancel out and you are left with no more 3's.


As for the 0th root, I can't help but think its not possible and will have something to do with dividing by 0, idk, I'll bring it up with my math teacher (who absolutely HATES even talking about dividing by 0)

[Daedalus]

Technically that is not correct, as you can't just have nothing.

Take this...

3/3 = 1

Now, according to your logic, the answer is 0, because the threes cancel out and you are left with no more 3's.


As for the 0th root, I can't help but think its not possible and will have something to do with dividing by 0, idk, I'll bring it up with my math teacher (who absolutely HATES even talking about dividing by 0)

No, because in that situation you're asking "how many threes are there in three?"

[Gamefandan]

No, because in that situation you're asking "how many threes are there in three?"

x⁰ = x/1*1/x = x/x = 1

Accept the truth.

[pocketrocket300]

Problematic.
A root of a number can be expressed as a fractional exponent.  So technically, the zero root is x^(1/0).
You can't have an undefined exponent.  It doesn't work out.

[Gamefandan]

Problematic.
A root of a number can be expressed as a fractional exponent.  So technically, the zero root is x^(1/0).
You can't have an undefined exponent.  It doesn't work out.

In saying this you also say that x⁰ = 1 is actually impossible. Learn to abstract mathematics.

[Mr. Wallet]

OK so Gamefandan dragged me in here to help.

It's easy to just say 0th root of x is x^1/0, call it all undefined, and be done with it. (Gamefandan: this does not conflict with asserting that x⁰ = 1. I have no idea how you came up with that idea.) However, in order to truly understand mathematics, especially as how it connects to the physical world around us, I feel that it's best to apply reason to what math actually means and only resort to notational juggling if it's strictly helpful for a calculation. So, what would the 0th root of a number actually mean?

The nth root of x is y iff yⁿ = x. That's what we literally mean and are necessarily talking about when we talk about roots.
If we want to find the 0th root of x, we must find a number y such that y⁰ = x. If we can find y, we have a 0th root.

The result should be blatantly apparent to anyone who knows what y⁰ is: The 0th roots of 1 are the domain of all real numbers, and the 0th root of any real number other than 1 is non-existent (undefined). The completely arbitrary nature of the 0th root of 1 was derived in the OP when Gamefandan showed that 0√1 = x for absloutely any freakin' god-damn x that's actually a number you can perform normal algebra on.

Since "all real numbers" is not a very practical solution in most applications of mathematics, and it applies only to rooting 1, we can generally summarize that "0√x is undefined" in most contexts including high school math tests.

[Kalphiter]

y iff

Excuse me?
Anyways, good point.

[Gamefandan]

Excuse me?
Anyways, good point.

Lolyiff.

For those who don.'t know what "iff" means: It's a way of shortening "If, and only if" and it simply means that it's a biconditional statement.

[Gamefandan]

I should do math threads like this more often.

[Gamefandan]

I triple post bump a thread about mathematics.

Hurr.


Oh god I just loving noticed I spelled 'mathematical' wrong in the title. God loving damnit.