Why is x^0 = 1 (Quick Proof)
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- čas přidán 26. 02. 2018
- Why is x^0 = 1? Proof
Using simple mathematical tools we can prove that x to the power of zero is 1 by dividing indices i.e (x^n/x^n) = x^(n-n) = x^0 and this is equal to 1 because any number divided by the same number is 1.
This is true for all values of x, except for the special case where x is 0 in which case 0^0 is undefined.
Music by Adrian von Ziegler
And this is what I call quick maths
That's not math. It's diachronic distortion of math.
I never thought this could be made understand soo easily and quickly.🔥🔥🔥
You have saved my life, mate
actually its not correct. x^0=1 by definition ! no need to proof
@@otoghost well my teacher told me I have to prove it so
@@just_panini1225 no need to proof like 0!=1 same
I love you rania
@@otoghost vaa qartvelo salami
This explanation is quite clear and to the point, great video :D !
and soothing music too!
x^0=n
multiply both sides by x
x=nx
divide both sides by x
n=x/x
n=1
substitute into original equation
x^0=1
Neutron fuck, just realised. i was a stupid bitch 2 months ago lol
El mero mero Loliconero - Looks legit to me! Nice proof!
@@smallnoob7577 What's the problem here?
@@harrylamont6007 😄😄😄😄🤣
How do you know that (x⁰)(x) should be x? You already assumed x⁰ as 1 there.
2^3=8
2^2=4
2^1=2
2^0=1
2^-1=0,5
2^-2=0,25
Divide by 2 each time. 2 could be replaced by n.
Some things are not meant to tell.
But just to show 🙂
What music is this mate I love it! :)
Music by Adrian von Ziegler
My teacher thinks I'm smart now, thanks bro
Now i can Rest In Peace
these are so relaxing
Yeah
0^0 is defined to be 1and it is not undefined. It is a convention that 0^0 is one. Bcoz, if this convention is not followed, then binomial theorem, geometric series, and many more theories in mathematics cannot work for some specific cases. EG: The infinite sum of geometric series is :
1/(1- x) = x^0 + x^1 + x^2 + .....
........(for |x| < 1)
Plugging x = 0, we get,
1 = 0^0 + 0^1 + 0^2+.......
Thus,
0^0 = 1 In most areas of mathematics such as set theory, algebra, etc
Mathematicians define it to be 1
Does that formula really have to limit itself to just x
You don't use "for e.g.", the for is unnecessary
Where did you learn this stupid math from?
0^0 means this:
0^x/0^x which means =0^0.
first statement is equal to 0/0 which is not undefined but indeterminate.
@@MusicIsLife-cd1xd What a vacuous scapegrace!! It's inutile to try to enlighten people who are bedecked by a donjon of incognizance.
@@srpenguinbr Thanks
The exponent of a number says how many times to use the number in a multiplication. That's the definition. So, if power is 0 then the result can be only 0. Yes, we all were taught the absurd x^0=1 but it's simply wrong by definition.
x^5 / x^3 = (x* x* x* x* x)/(x* x* x)
=x^2
In general, x^n /x^m = x^(n-m)
Let m=n, this property should still hold.
x^n /x^n =x^(n-n) =x^0
Any number divided by itself is 1, x^0 =1.
1 is, in a sense, to multiplication what 0 is to addition. They’re the identity element , meaning x* 1=x and x+0=x.
Not wrong by definition, it makes sense that if adding no numbers at all gives back the additive identity, multiplying no numbers at all should give the multiplicative identity.
@@CruzRedeemer Do you need a rule for the case you divide the same things??? Isn't obvious the result is 1?
@@CruzRedeemer Nothing can't be equal to 1. Don't you have common sense?
Tell me, 1^0 + 2^0 + 3^0 +... inf^0=?
Its because the value of x is 1 and x has an invisible 1 and if u times 0 by x the x will dissapear and the only thing that is left is 1
You have solved this through quick math using the division can't we do with this multiplication....
Let me clear this
1⁰=0
Can we say that 1⁰/1=0
1⁰=0/1×1
So left is 1⁰=0 / Questions- when we write a number after infinite zeros like 000002374 it has no value like hundreds thousands million trillions etc etc... but it can have its value on LHS before zeros like 2374000000...0 ans so on. WHY? CAN ANYONE ANSWER?
Can you explain why you have done division when it has asked to to multiplication as power raised by 0 then it should be multiply not divide
We may proof it in another way
i.e
To prove; X^0 = 1
Poof;
Let A = X^0 ------(i)
taking log both side , we gate
log(A) = log(X^0)
log(A) = 0log(X)
log(A) = 0 ------(ii)
since log(1) = 0 -------(iii)
from equation (ii) & (iii) we get
A = 1
by putting it in equation (i) we get
X^0 = 1
#HENCE PROVED
like it if you are getting/understood my concept.
You can't prove equation 3, the only reason we know that log(1) = 0 is because of the rule that x^0 = 1. If you expand equation 2, then you get 10^0 = A, which is the equation we are trying to prove.
It's very helpful... Thanks for providing such a video.
X0 could be interpreted as a (1) point. (X1 - line, X2 - area, X3 - volume)
Damn! I understood it within 18 seconds!
The background music made my family think that someone was calling
the n's cancel out. Mind Blown.
You Sir, are amazing.
Nice!
holy crap you just made my brain click instantly
Thank you for your explaination
Very good video, thank you bro.
Ah thank u very much.
damn.
Why will we divide why not into
We divide it because a^n÷a^n becomes a^n--n if we multiply a^m × a^m it becomes a^m+n
Example with take a^1÷a^1 = a^1-1 becomes 0
And if we multiply a^1 × a^1 = a^1+1 which equals to a^2
I hope this helps you 😊
thank you very much I really appreciate it
I will be first person to define 0^0 .. 😌
Best of luck dude
Thanks
Thanks.. Oh, Finally understand this
It still feels illogical, x is multiplied by itself zero times so where did the 1 come from?
Sorry to say you don't prove anything at all! On both sides of "=" symbol, you must have objects of same nature, and no one know is a^0 is a number ! What does it mean "to multiply the number a, zero times by itself" ?
SO we must ADMIT that convention, to keep further calculations (with powers) consistent
Thank you
👍
Thanks😎
man thank you
This only quick .40 sec save my voice as well as my eyesight😅🤭....thanks bro👍
I can assume you're a teacher, but why did it save your eyesight?
Is 0 power to 0 equal 0 or considered undefined
Undefined cause you can't divide 0 by 0
@@iuse4rchbtw:
0² ÷ 0¹ ≠ 0²⁻¹
a⁰ = 1, a ≠ 0
no if a≠±∞
big brain time
real life example for a^0=1.
Aah I finally understand
Very good
oh
This is only when x is a non-zero. But what if x is 0?
1
0⁰ = 1, but unlike any other X, 0⁰≠0/0
Nice
But this definition doesnt work for x=0
Awesome......👍
I have a question then. X^0 represents that x occur 0 times. Now if x=1, that means 1 occur 0 times. Then how is 1^0=1
lol
0^(0) = undefined
1
That was great
But same number/ same number =1 is not true for 0/0 ????🙄🙄🤔🤔
wow thank you i always was like whaaat now it makes sense.. more sense.
Maths OP
x⁰ = 1 does not require a proof, because it is part of the *definition* what the expression x^n means.
x^n, where n is a natural number or zero, is *defined* as x^n = 1 * x * x ... * x with n factors of x. For n = 0 one thus gets immediately x⁰ = 1 as a special case of the *definition* of x^n.
Alternatively, one may define for natural numbers n (not including 0) that x^n = x * x ... * x with n factors of x. This leaves it open what x⁰ is and hence one needs an explicit statement that x⁰ = 1 as a second part of the definition. Again, x⁰ = 1 is part of the definition of x^n.
If you think the 1 in the first definition is strange, consider the definition of x^(-n) (where n is a natural number or zero and x 0), which is x^(-n) = 1 / x / x ... / x with n divisions by x. Here one definitely needs a 1 to start with, so there is nothing unnatural about starting the definition of x^n with a 1.
Where did you learn this stupid math from?
0^0 means this:
0^x/0^x which means =0^0.
first statement is equal to 0/0 which is not undefined but indeterminate.
Show me by numbers not letters plz
Explain for me simplest way! Use numbers plz
@@techamcchannel4913
2^3 = 1 * 2 * 2 * 2 = 8 (there are 3 factors of 2)
2^2 = 1 * 2 * 2 = 4 (there are 2 factors of 2)
2^1 = 1 * 2 = 2 (there is one factor of 2)
2^0 = 1 = 1 (there are zero factors of 2)
If the 1 at the beginning of the product seems strange consider in analogy:
2^(-3) = 1 / 2 / 2 / 2 = 1/8 (there are 3 divisions by 2)
2^(-2) = 1 / 2 / 2 = 1/4 (there are 2 divisions by 2)
2^(-1) = 1 / 2 = 1/2 (there is one division by 2)
2^0 = 1 = 1 (there are zero divisions by 2)
@@christianborgelt8318 thanks for honesty answer.
1X= kitna hota hai
Another reason:
n^(a+b)=(n^a)(n^b)
and
x+0=x
and
1x=x
so
n^(a+0)=(n^a)(n^0)=n^a
therefore
n^0=1
But 0^0 is also 1
Can't divide by 0
Thanks..super..
O.g ty
Why (-1)×(-1)=1 ?
2 negative numbers multiplied together will alway's produce a positive result. This is the same as 1x1.
I know but I want proof . Now I found it.
@@kashmirdhankhar6003 the internet is literally there for your proof or go figure it out yourself. It's best to do the latter since then you can justify with your own findings why a negative*negative = positive
I can do it IN ONE SINGLE STEP.
What The Haven! It was that simple!
Ohh......
Is there a proof for this concept that uses non circular logic?
a>0
Wrong
#exponents
Singhania?
we could've just applied log on both sides :)
log x^0 = 0 log x =0|||||||||| Log1=0
proved !
log 1 = 0 is defined from the fact that x^0 = 1
@@mxpph yeah you are right
Your proof is wrong.
To demostrate that x^(n-n)=(x^n)/(x^n) you need to know that x^0=1.
(x^m)/(x^n)=(x*x^(m-1))/(x*x(n-1))=.....=x^(m-n)/x^(n-n)=x^(m-n)/x^0=x^(m-n)/1=x^(m-n)
Thus, to proof that x^0=1, you need to know that (x^m)/(x^n)=x^(m-n) whose proof makes use of x^0=1.
No, proof right.
This is not a proof for why x^0 = 1, rather this is a proof that x^n/x^n always equals one no matter what numbers you put for n or x
Right
😂😂COME ON
This isn't really a proof, it is just statements that arise if you assume that x^0=1 from the beginning. What I'm saying is how do we know that(x^n)/(x^n)=x^(n-n) is true when n=0? It's like you are assuming that x^0 is a real number from the start.
0:43 Not gonna lie, I was waiting for that and would have downvoted if it did not come.
This doesn't work for x=0
Yeah, but 0^0 is still 1
@@Ostup_Burtik I agree
Nope. 0^0 is also 1.
x/x is 1 only if x is not already 0 .... so that proof is a bit cyclical ...
but how will be solve if X=0,because 0÷0=not defined
Hi Akhilesh, you're correct! but I did include that case at 0:42 of the video. 0 is an exception
why x is exception
I'm not sure if there really is a reasoning for the exception apart from the entire proof collapsing because of a singular case in an infinite number line. Exceptions often occur in mathematics, for example if I were to ask you to graph 1/x, you can graph it for every x value except x = 0, does this mean the graph doesn't exist? of course not! so just because there is an exception, doesn't mean the entire process is invalid. Hope this helps
For x=0
It's called indeterminant term aise 8 cases h maths me jinme ans nahi aati uske liye pehle aisi terms ko determinant term me convert karna padta h aur fir solve karna padta h
& Simple maths me aise terms aati hi nahi h it cames only in derivation & limits
What is you have an imaginary number for X?
Using the same kind of trickery: 4 = 8^1 / 2^1 = 8^1-1 / 2^1-1 = 8^0 / 2^0 = 1/1 = 1. So 4=1. Silly, yeah, but no more sillier than this 'proof'. Just stop this nonsense and come clean : mathematics needs x^0=1 for it to work so it makes up all these tricky little ways of justifying its choice.
It is a wrong proof.
No
*clown song on*
bih no subtb huh! fx no!!!%#soulja
fr
but 0/0 doesn't = 1
Anyone gonna point out how most of the comments r asian people lmao
X^0= 1, X≠0 is BY DEFINITION.
You don't prove it.
Your "proof" was actually just a demonstration for why it is a good idea to define X^0 = 1.
no 0^0=1
very bad video i didnt understand and no im not dumb
So bad
Wrong, x⁰ = ∞
Infinity is not a real number, but it does exist
True 🥱
Thanks
Thanks
Thanks
Thanks