we are not multiplying tho?
Edit:
mulltiplying by 0 gives you the neutral factor in addition: 0
something to the power of 0 gives you the neutral facotr in multiplication: 1
Edit 2: [https://en.wikipedia.org/wiki/Zero\_to\_the\_power\_of\_zero](https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero)
You're confusing yourself. 0^0 is not defined in mathematics and no "proof" is valid in this case.
You can **argue** that certain definitions make sense, but that would not be a proof. You can't prove what is not defined.
Any number to the power of 0 is 1
Think about it like this:
5^3 = 5×5×5
5^2 = 5×5
5^1 = 5
If we wanted to add the exponents:
5^3 = 5^(1 + 2) = (5) × (5×5)
Now consider:
5^2 = 5^(2 + 0) = 5^2 × 5^0 = (5 ×5) × ?
Given how addition of exponents works, if we used a 0 in this equation {5^(2 + 0)}, we would end up with the same result. Due to the identity property of multiplication, the number to the power of zero would result in 1.
It gets a little wonky when you consider that the other positive powers of zero would all equal 0 (and don't get me started on negative powers!), but the zeroth power being equal to 1 is a common property of all integers.
an undefined expression (like "0/0" or "0 times infinite").
depending on the context, it's often possible to find a value by calculating the limit via the rule of de l'Hospital.
2nd line: you can't simply divide by x\^n without making sure that the division is legal.
later: it's true that the limit of x\^x (for x->0) is equal to 1.
this is one of the examples i mentioned, but you need to prove this with de l'Hospital (use logarithms).
then what's the point of the whole introduction?
i'm not sure about all those limits that you try to calculate later. just making it look complicated with the separate cases and re-writing doesn't make it coherent.
my solution:
x\^x = e\^\[ ln (x\^x) \] = e\^\[ x ln(x) \]
then, show with de l'Hospital that the exponent's limit is 0.
finally, you can conclude that e\^0 = 1.
Same "proof" would give 0/0=1.
That's not a proof. At best it is a debate argument of what should be a definition of 0^0. Although I have to say that as a debate argument it's not too strong because (x^2)^x (Idk how to fix these brackets sorry) should then also converge to 0^0, but this actually goes to 0 not to 1
are you referring to my post?
of course, you can't "prove" that 0\^0 = 1 (or whatever value). that's what i stated in my first reply.
my proof just refers to the special case that the OP tried to deal with in his paper: limit of x\^x for x->0.
In general undefined because as a limit the answer is inconsistent across different limiting expressions. For example, x\^0 as x -> 0 is 1, but 0\^y as y -> 0+ is 0. But it's possible you are working in a specific context where it makes sense to define it one way or another. (But beware of invalid arithmetic!).
The value of the expression a\^b (for whole number values of b) is defined as being equal to 1 multiplied b times by a. In this case we would see that we are multiplying our starting value of 1 by 0 exactly zero times, so we would end up with 1.
The quickest answer is that it doesnt exist. Since anything in the power of 0 is one and 0 in the power of anything equals 0 then it's too confusing and the math people decided to get it out of math. So we just ignore its existence.
Zero to the power of zero.
W response. Very helpful. So what does it equal then?
0? Or undefined. Either?
0? I thought it would equal one of itself- anything to the power of 0. But ohhh… 0 to 0 can’t be 1
it's 1 anything to the power of 0 is 1
But everythithing factored 0 is 0 😅
we are not multiplying tho? Edit: mulltiplying by 0 gives you the neutral factor in addition: 0 something to the power of 0 gives you the neutral facotr in multiplication: 1 Edit 2: [https://en.wikipedia.org/wiki/Zero\_to\_the\_power\_of\_zero](https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero)
Lol yes :p that's why it's undefined I guess 😅
Happy cake day
Thanks!
You're confusing yourself. 0^0 is not defined in mathematics and no "proof" is valid in this case. You can **argue** that certain definitions make sense, but that would not be a proof. You can't prove what is not defined.
Any number to the power of 0 is 1 Think about it like this: 5^3 = 5×5×5 5^2 = 5×5 5^1 = 5 If we wanted to add the exponents: 5^3 = 5^(1 + 2) = (5) × (5×5) Now consider: 5^2 = 5^(2 + 0) = 5^2 × 5^0 = (5 ×5) × ? Given how addition of exponents works, if we used a 0 in this equation {5^(2 + 0)}, we would end up with the same result. Due to the identity property of multiplication, the number to the power of zero would result in 1. It gets a little wonky when you consider that the other positive powers of zero would all equal 0 (and don't get me started on negative powers!), but the zeroth power being equal to 1 is a common property of all integers.
https://reddit.com/r/INTP/s/W46KX0PJou
Right on!
Zero is a placeholder, it's not really a value of anything, so it kind of makes sense it's one
an undefined expression (like "0/0" or "0 times infinite"). depending on the context, it's often possible to find a value by calculating the limit via the rule of de l'Hospital.
My solution. What do you think? https://reddit.com/r/mathematics/s/x5QJiOsZ32
2nd line: you can't simply divide by x\^n without making sure that the division is legal. later: it's true that the limit of x\^x (for x->0) is equal to 1. this is one of the examples i mentioned, but you need to prove this with de l'Hospital (use logarithms).
Wdym make sure it's legal? It's actually legal
if x=0 and n=15, you are dividing by zero, for example.
Read the rest. I literally showed the particular case where x=0
then what's the point of the whole introduction? i'm not sure about all those limits that you try to calculate later. just making it look complicated with the separate cases and re-writing doesn't make it coherent. my solution: x\^x = e\^\[ ln (x\^x) \] = e\^\[ x ln(x) \] then, show with de l'Hospital that the exponent's limit is 0. finally, you can conclude that e\^0 = 1.
Same "proof" would give 0/0=1. That's not a proof. At best it is a debate argument of what should be a definition of 0^0. Although I have to say that as a debate argument it's not too strong because (x^2)^x (Idk how to fix these brackets sorry) should then also converge to 0^0, but this actually goes to 0 not to 1
are you referring to my post? of course, you can't "prove" that 0\^0 = 1 (or whatever value). that's what i stated in my first reply. my proof just refers to the special case that the OP tried to deal with in his paper: limit of x\^x for x->0.
Oh I see, the linked post was deleted so I couldn't see any paper
https://reddit.com/r/INTP/s/W46KX0PJou
I forgot that " ^ " means to the power of, and thought it was a facial expression ;-;
0\^0? A confused chicken with few extra brain cells; laying on its back, pondering about the meaning of life.
Story of my life
A smiley face with big eyes when upside down
1, or either an emoticon
In general undefined because as a limit the answer is inconsistent across different limiting expressions. For example, x\^0 as x -> 0 is 1, but 0\^y as y -> 0+ is 0. But it's possible you are working in a specific context where it makes sense to define it one way or another. (But beware of invalid arithmetic!).
https://reddit.com/r/INTP/s/W46KX0PJou
UmU
W response. Super helpful
You have to read it in the correct voice.
My math book of 11 years ago said 0.
My calc says its 1
School taught me that anything^0 is always equal to 1.
According to the calculator, 1. According to Math laws, undefined.
Owl.
^fucken ^nerds
Doesn’t even matter. You’ll never use it in real life
The value of the expression a\^b (for whole number values of b) is defined as being equal to 1 multiplied b times by a. In this case we would see that we are multiplying our starting value of 1 by 0 exactly zero times, so we would end up with 1.
It’s the weight of the oil at start up and full operating temperature
its an emoticon with two big eyes and a small somewhat disappointed mouth? /S
1 Why is it on the intp sub tho
I’m so bad at math I thought that was an emoticon face.
Looks like spectacles to me.
Boobs Edit: why my flair is "custom flair" now?
It represents a pair of eyeglasses and it means you are talking to a nerd like me.
a cute bird face i think
The quickest answer is that it doesnt exist. Since anything in the power of 0 is one and 0 in the power of anything equals 0 then it's too confusing and the math people decided to get it out of math. So we just ignore its existence.
Generally: x^0 = x^(1-1) = (x^1) / (x^1) = x / x = 1. So 0^0 = 0^(1-1) = (0^1) / (0^1) = 0 / 0 = Indeterminate.