I hate Maths because it's confusing sometimes n⁰ =1 0ⁿ = 0 but

what is 0⁰?

L hospital 😅😆

0^0 is undefined in most mathematics.

It's undefined, but the agreed value is 1, until proven otherwise

Wolfram has different view of the world of that madness

Wolfram alpha limits are calculated using algorithms. 0^0 is indeterminate. The value depends on what f(x)^g(x); f(x) -> 0 and g(x) -> 0 you take. As for the function x^x in question, lim x^x i can make this a inf/inf form by transforming it into e^lim(lnx/1/x) Using l hospital rule e^lim(1/x/-1/x^2) e^lim(-x) e^0 1

was checking on the graph actually. Wolfram has better precision than most languages

It is still an approximation

true. but atleast it beats my calculator on the nearest to zero it can reach

Lol, calculators can do some weird shit as well haha. I remember a video, lemme find it

n^(0) = n^(1-1) = n^(1) * n^(-1) = n * (1/n) = 1 if n != 0 then n^0 = 1 But when n = 0, (1/n) is undefined so we calculate its limit to find out what it could be lim n * (1/n); n -> 0; = 1 Because when its approaching 0 and its not equal to 0 it behaves like other numbers we cancel n out and get 1 as a result

This is not correct, taking a function which is of the form 0^0 and then taking it's limit is not the way to determine the value 0^0 approaches to Take this expression for instance, (e^(-1/x))^x this approaches 0^0 as x = 0 As x->0 lim(e^(-1/x)) = 0 As x->0 lim(x) = 0 But lim(e^(-1/x))^x = 1/e as x -> 0 And not just this, there are thousands of ways you can approach 0^0 and end up with a value different than 1 0^0 is an indeterminate form. By definition it is a form which can't be evaluated by replacing sub expressions by their limits The reason 0^0 is agreed to have the value of 1 because a lot of the theorems hold true for this value. There isn't a formal proof yet to this and trying to prove it using limits is not correct

x^n can be interpreted as multiplying 'x' to itself for 'n' times (or, is that wrong?). As per this, 0^0 should be 0 only, right?

Yes but when someone hates math you dont explain to them using e and limits involving powers

I guess :) but still that can cause misunderstanding in the longer run

No, x^0 is a weird thing. It is an extension of the definiton x^n = x * x * x... n times * x Where x and n are whole numbers

0^0 is an indeterminate form

that's not how limits work

I was not even talking about limits, it is an agreed value, read this: https://t.me/c/1142198149/502174

i don't think there's a point to having an "agreed upon value" for an indeterminate form

It has value, for instance binomial expansion of (1 + x)^n makes sense for x= 0 and n= 0 That value is also used in computer science so you woudn't have to write a special case for 0^0

you mean x=-1?

Yep.

it's probably because the limit is 1 in that case :/ and not because the limit is usually 1

That's not how limit works as you said youtself. Limit of an indeterminate form heavily depends on the way you approach it.

^ he last two paragraph. I think I am quite clear here

huh i thought any equation with x→0 had a fixed limit (1/e in this case)

I don't understand what you're asking about here.

you're saying limit depends on approach, I'm saying limit is fixed

For an indeterminate form its not. Take x/sinx as x->0 And Take x^2/sinx as x->0 Both are 0/0 indeterminate forms, Both will have 0/0 at x = 0 But their limit is different lim(x/sinx)= 1 lim(x^2/sinx) = 0

I'm not saying 0/0 is always 1 (that's what you're saying, for 0^0 to be agreed to be 1) I'm saying eg. sin(x)/x for x->0 is always 1, that's correct at least, right?

I was just saying that some mathematicians agree that 0^0 is 1, it is not the actual value as it is undefined Yes lim(sinx/x) as x-> 0 is always 1

those mathematicians should be told that newton didn't die to hear this shit

There are research papers about it. And for discrete mathematics it can make sense as a lot of algebraic expressions tend to give that value.

yeah well, not explaining in a paper why you took a 0^0 indeterminate's value to be 1 is alright, can't explain everything in a paper but at least it is provable in those cases right? instead of just assuming it

Newton was against Cartesian geometry and he was an alchemist dedicated to find secret messages from God in the Bible

Einstein smoked weed

Yes, but what I meant is that Newton was kind of a bullshit factory

his papers weren't bullshit tho

I guess 🤔, they must have done some empirical proof or something.

You mean perspective geometry?

No, anything that has to do with a Cartesian graphs

Netwon's work was heavily based on cartesian geometey

Yet he found it inelegant

Oh okay, i've read his work pushed forward eculidian geometry replacing perspective geometry which used to be an important subject

Then what I read is false, thanks for the info

Here, you might find this interesting: https://youtu.be/NYK0GBQVngs

nerd

:( i like mathematics

I'll watch it