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We learned it's an undefined valueAs 0 to the power 0 looks like 0/0 But for Euler, he considered that 0^0 =1 (in his book "Introduction to Analysis of the Infinite")There is no consensus among mathematicians about that..

but doesn't the limit from the negative approach negative 1?

No. It approaches a complex number. The real part approaches 1. The imaginary part approaches an infinitesimally small negative number.

Any base raised to zero always equals to one. Also, zero raised to any exponent is zero. But by taking limits closer to zero let's say 0.00000001 base to the power of 0.00000001 is equal to 0.999999 which is closer to one.

But since no value given current information, ie the expression does not determine original limit, so should be indeterminate and leave it undefined? Correct me if I'm wrong.

In short, from the perspective of mathematics, this is undefined.

I'd show him my phone ad hope he doesn't notice the question at the bottom -

https://en.wikipedia.org/wiki/Exponentiation#Zero_exponentBy definition, any nonzero number raised to the 0 power is 1:[16][1]b^0 = 1.This definition is the only possible that allows extending the formulab^(m+n) = b^m . b^nto zero exponents. It may be used in every algebraic structure with a multiplication that has an identity.Intuitionally, b^0 may be interpreted as the empty product of copies of b. So, the equality b^0 = 1 is a special case of the general convention for the empty product.The case of 0^0 is more complicated. In contexts where only integer powers are considered, the value 1 is generally assigned to 0^0 but, otherwise, the choice of whether to assign it a value and what value to assign may depend on context. For more details, see Zero to the power of zero.https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero

0⁰ x must be equal to x. As it means that you multiplied 0 to x zero times. That is you never multiplied 0 to x. Hence x stay as it is. In that case 0⁰ has to be 1 for sure.

Here's an unconventional approach.Quote0⁰ x must be equal to x. As it means that you multiplied 0 to x zero times. That is you never multiplied 0 to x. Hence x stay as it is. In that case 0⁰ has to be 1 for sure.

Garbage.

y = x^{x} is well-defined for all x < 0.

I'm not sure how unconventional that is. As I say in my previous post (which crossed with yours), this is how I was taught to think of this in school (8th grade, I think?)

Great video, but it doesn't in any way show that 0^0=1, the real answer is undefined. That is about the limit of X^X in R+ as X approaches zero. In fact with with that kind of reasoning you might even argue that the answer is 0 because the same limit on R- is -1 (so 0 on average)

(-0.0001)^(-0.0001) = 1.00092141 - 0.000314448745 i

Quote from: Petrochemicals on 02/11/2021 07:32:02Garbage. Someone's trash is someone else's treasure.

Quote from: chiralSPO on 02/11/2021 06:03:12y = x^{x} is well-defined for all x < 0.What does it mean? Doesn't it mean all negative x?

Quote from: hamdani yusuf on 02/11/2021 09:40:20Quote from: Petrochemicals on 02/11/2021 07:32:02Garbage. Someone's trash is someone else's treasure.4^0.5=24x(4x0.5)=8(4x0.5)x(4x0.5)=44x(1÷0.5)=84^(1÷2)=24^1/2=2Square root 4=2Square root( 4^1) =24^3/4=2.828etcQuad root (4^3)=2.828etc.

So basically you are looking for a root if the number drops below the whole number.

But asking for a root of zero is nonsense for the same mathematical reasons that there are no positive square numbers. But a zero root of a number is one?

0 + 0 = 0.0 * 0 = 0.0 / 0 = 1.0 ^ 0 = Undefined.0 - 0 = Nothing.Ps - Dyscalculia!👻

Quote from: Zer0 on 02/11/2021 14:06:290 + 0 = 0.0 * 0 = 0.0 / 0 = 1.0 ^ 0 = Undefined.0 - 0 = Nothing.Ps - Dyscalculia!👻I would switch the third and fourth: 0/0 = undefined and 0^{0} = 1