Patreon: / h3vtux My attempt at making an instructional visual explanation. Music is by Eric Prydz.
Пікірлер: 418
@cakeandicecream15829 ай бұрын
It’s nice to see someone explain something simple in the most convoluted way possible. Usually teachers try to do the opposite, so it’s refreshing to see something a little different.
@H3Vtux9 ай бұрын
You're welcome!
@esthersandoval13453 жыл бұрын
Thank you so very much. This explanation is one that is so needed in order to understand this concept. If only middle school teachers would explain how to arrive at the answer of "one" when a number to the power of 0 is 1, then students would have logical procedures in arriving at an answer that makes sense instead of just repeating or memorizing that the answer is 1. Excellent. Loved the video.
@thenetsurferboy5 ай бұрын
I never saw a number to power 0 in my 16 years studying maths
@bahmannosratollah7017 Жыл бұрын
unbelievably easy explanation. easy to understand. Thank you.
@H3Vtux Жыл бұрын
Thanks man, this was actually my first teaching video so it's nice to see people stumble upon it every now and then. I'm glad it helped!
@garyfinch7337 Жыл бұрын
Thank you. Nobody has ever explained it so clearly and simply as you have, and for the reason that it has to be so. If they had, 40+ years ago, when I was at school, I might have had a more positive attitude to maths. As it wasn't explained to me, my attitude to maths, was akin to my attitude to religion; skeptical of anything that did not prove itself and was the only possible choice available. Thanks again, Gary.
@RahulShah-oh7oh11 ай бұрын
Me bhi maths ke vedio banata hu aap dekhe or comment kre youtube.com/@RKEVEDIO?si=dSkOtJxP-JiNfI4v
@bradleystoll69116 жыл бұрын
No one in the field of mathematics is debating whether 0^0 is 0 or 1. We are all sure that 0^0 is in fact not defined. Also, exponents are closely related to logarithms. In fact, in the history of mathematics you will find that logarithms have been around longer. Once one has defined the natural log function via the an integral (which is how many believe it should be done), then proving a^0 = 1 for all a > 0 is a trivial task.
@bryan95876 жыл бұрын
Bradley Stoll Oh ffs. Just because YOU are not debating that topic, doesn't mean real mathematicians aren't either. Calm down, kid.
@bradleystoll69116 жыл бұрын
I'm not sure what a "real mathematician" is, hence I did not use that terminology. Maybe I am, maybe I'm not. I've heard many math educators (at the college level, even) say that everyone is a mathematician. Through my undergraduate and master's in math, and now as a teacher of calculus for 22 years, I've never come across anyone, or read any math text book, or other related math book, that has entertained the idea of 0^0 being equal to 1. I could certainly why one would want to DEFINE 0^0 as being one, from the basis of limits, but I could define anything I want and it doesn't necessarily make it correct. I'd love to hear more about this debate (other than on KZbin!, or read where people want this is being discussed, so if you could, please direct me to the some reputable literature on this. I'd be curious if these (people) are debating that 0/0 - 1, also. I suppose this would explain a lot. I recall two instances that got me riled up, albeit early in my teaching. One was an elementary school teacher telling me that the sqrt(4) = +/-2. I tried explain that it wasn't, it was only 2, as the sqrt symbol implied only the principal (positive) root, but they were having nothing of it. I tried my best to explain why x^2 = 4 has two solutions, one positive, one negative, and showed two different ways to see that. Alas, it was a futile effort, so I gave up. Next, was someone who was convinced that sqrt(x^2) was x and not absval(x). Even after I showed examples of negative x's they just would not let their false thinking go. But, that doesn't mean one couldn't define sqrt(x^2) as x...they'd just be living in a completely different world (ie, their own) of mathematics:). Oh, I appreciate being referred to as a "kid." Many have said I look young for my age (I am over 50)...and I'm not a billy goat, either:).
@Vaaaaadim5 жыл бұрын
@@bryan9587 I know these are old comments but. Indeed, there is no debate about whether 0^0 is 0 or 1. It's considered to be an indeterminant form. You can construct examples where 0^0 becomes 1, or 0, or anything actually. Take for instance, these two functions, both become 0^0 at x=0, but one of them goes towards 0, and the other towards 1. www.desmos.com/calculator/box5zwu1w8
@careydedo36215 жыл бұрын
@@bryan9587 What are you even doing here?
@MuffinsAPlenty5 жыл бұрын
I would agree that no one in the field of mathematics is debating whether 0^0 is 0 or 1. On the other hand, I disagree with the conclusion that we are all sure that 0^0 is in fact not defined. It all depends on context - in particular, what does "exponentiation" mean? Depending on what exponentiation means, either 0^0 = 1 or 0^0 is undefined. For example, you can look up the set theoretic construction of the natural numbers (which includes 0 as a natural number) and look up the set theoretic definition of natural number exponentiation. For two natural numbers n and m, n^m is defined as the natural number in bijection with the set of functions from m to n. In the case that m = 0 and n = 0, there vacuously exists precisely 1 function from the empty set to itself. Hence, by this definition 0^0 = 1. Generally, whether 0^0 = 1 or 0^0 is undefined depends on whether exponentiation is viewed as a discrete or continuous operation. In virtually every discrete context, 0^0 = 1. The reason for this is that, in the discrete context, exponentiation represents repeated multiplication. As such, x^0 is a product with no factors, i.e., the empty product, regardless of the value of x. The empty product is defined based on the associative property of multiplication, and hence, has a value of 1. On the other hand, if you're in a continuous context, then exponentiation is defined in terms of limits or logarithms, as you suggest. In such contexts, the definition of exponentiation does not allow 0 as a base to be raised to virtually any power. As such, 0^0 is left undefined. If you teach a calculus course, it makes sense to state that 0^0 is undefined, since you don't want students to say that their limit is 1 when they get the indeterminate limiting form of 0^0. Of course, things then become awkward when you get to power series and have to use 0^0 = 1 there. Of course, you _could_ try to explain why 0^0 should be replaced with 1 in the context of power series in a number of ways, but it fits nicely into the discrete context there, since the exponents of x in a power series are discrete exponents representing repeated multiplication.
@slimshady4life689 Жыл бұрын
This was extremely helpful. I'm currently teaching myself Electrical Engineering and the book I'm using did not explain this and I was very confused. Thank you so much.
@xNiGHT9616 күн бұрын
Not only that it was explained clear and concise, but It was also explained in a simple way, apart from what I've seen till now (and I have watched some videos in this particular subject). Love it, I am looking forward on this channel if I encounter another misconception. Thank you!
@RaaZVan995 жыл бұрын
I think an easier way to explain this would be this a^x/a^y = a^(x-y) => a^(n-1) = a^n/a; Let a=2 and let's start with 2^4 = 16; 2^4 = 16; 2^3 = 2^4/2 = 16/2 = 8; 2^2 = 2^3/2 = 8/2 = 4; 2^1 = 2^2/2 = 4/2 = 2; 2^0 = 2^1/2 = 1; And moving forward, that's why 2^-1 = 2^0/2 = 1/2, etc;
@oDuckology5 жыл бұрын
so basically it's a geometric sequence where the values get divided by the base
@ItzPinecone5 жыл бұрын
excuse me WHAT
@kumoki5 жыл бұрын
no I don't understand whaaat
@andressstyle63904 жыл бұрын
@Lukas yea, it should ... Anyway, it's the same demonstration showed in the video .
@lumen27054 жыл бұрын
weird flex but okay lol
@DigilusionStudios3 жыл бұрын
Sometimes you just need to find someone that can explain things in different ways to learn it, Thanks.
@H3Vtux3 жыл бұрын
Thanks man, i'm glad it helped!
@princegupta81406 жыл бұрын
Amazing.....make more video like this...plz
@mollymolster75863 жыл бұрын
This was sooo helpful .I feel like sharing this with everyone I know but that would make me SERIOUSLY nerdy. lol.
@BoahYo Жыл бұрын
I was thinking about this and came to the same conclusion as the video. Just wanted confirmation
@starpaw2000 Жыл бұрын
Thank you so much for this video, It was briefly talked about in my math glass but for me to understand something I need to know WHY, and this video explained it very well. Have a great day!
@cancionesdeyu Жыл бұрын
0: OMG!!! I was stuck on this for so long! I FELT SO DUMB BUT THANK YOU SO MUCH FOR CLEARING IT OUT!!😭
@RealityCheck6T93 жыл бұрын
I can't compliment your videos enough, they're wonderfully explained.
@mysticcyber38403 жыл бұрын
Amazing!!!😅 This Video has single-handedly answered my lifetime's question or one of them, and my answer is that invisible 1 that no other video told me about. 😭Bravo *claps*
@H3Vtux3 жыл бұрын
Thanks I appreciate the feedback, I'm glad it helped!
@dzee1273 жыл бұрын
@@H3Vtux I absolutely second MysticCyber's re both the applause and the importance of mentioning the "invisible 1". Could you please put a link to some of the articles/debate you mentioned at the end of the video though? I'd love to learn about them and also help me understand why negative exponents results in fractions of 1. Thank you so much!
@TheZmoliver4 ай бұрын
Thank you! It's one of things I've always wondered about. It's like, you can go through entire courses and never have to know WHY it's this way (which usually means just taking someone's word for it). But I don't like to ever do that. I have to see it for myself. Thanks again!
@buttermilkpancakes9163 жыл бұрын
Omg thank you so much !!! 😭 this helped me out greatly.
@user-zf8gy1yw1p3 жыл бұрын
Another way to prove that a^0=1: a^n / a^n = 1 because anything divided by itself is 1. But, if you apply one of your exponent rules...: a^n / a^n = a^(n-n)= a^0 = 1, because of the first line.
@dragoncat57672 жыл бұрын
Thanks,much easier explained
@why87782 жыл бұрын
damn
@artemisiavelvet2046 Жыл бұрын
Nice. In that case "a" must be > 0
@princegonzales48072 жыл бұрын
If isn't here im gonna go to bed with my anxiety again
@indyjoe62 ай бұрын
the breakdown at the end was excellent
@hello-yk4hn2 жыл бұрын
Another way of proving it: 1 =64/64 =4^(3)/4^(3) =4^(3-3) =4^(0)
@TheVideoMaker19996 ай бұрын
This would be the turning point for him
@xaviercomelli5 жыл бұрын
Thanks, great explanation!
@adriasorensen22492 жыл бұрын
2^0 =1 which could stand for the number of points in a dimension. For example 2^0=1, so 0 is the dimension and 1 is the point in the zeroth dimension. Then, 2^1=2 which would be the 1st dimension that has 2 points on a line. 2^2=4 which equals the 4 points on a 2D square for the second dimension. 2^3=8 which would be the 8 points on a 3d cube in the third dimension. 2^4 = 16 which would be the 16 vertices on a 4 dimensional cube or tesseract....then, a 5d cube has 32 vertices (2^5=32). etc
@marka.2004 жыл бұрын
Fantastic! I needed to explain this to my teenage son learning about exponents (his teacher just did the hand wave and called it good), this video is a perfect explanation for him. Thanks!
@mayattv49864 жыл бұрын
Wtf. Sue the teacher lol
@handleisntfkinavailable2 жыл бұрын
The teacher probably didnt know why, he prob just accepted that anything ^0 is 1 without questions
@geet.ikagupta3 жыл бұрын
Thanks a lot...u solved my confusion in just 10 sec ❤️ !!!
@theloveofreading35632 жыл бұрын
I bet the first person to figure this out was excited !
@kevincassidy7233Ай бұрын
Any number divided by itself is 1. It's essentially the base unit for multiplication.
@subscreibe_productions5 ай бұрын
OMG ITS SO HELPFUL I COULDNT LIFE OF ME FIGURE THIS OUT
@z-inkp64783 жыл бұрын
4:50 is when it all made sense. great video though.
@bramk6720Ай бұрын
Incredible!! I dont seem to remember these math rules if they dont make sense to me and its also not any fun that way. I wish everything could be explained like in this video. I would never forget a thing. Thank you so much, this was fascinating 😁😁
@B.W.Bricks_productions Жыл бұрын
At 1:18 you said that it's being multiplied by "well, 1" and I don't follow. It seems like it should be they should be multiplied by each other.
@jallipallisaipraveenkumar18015 жыл бұрын
Thank you very much sir We still hope more videos from you of such questions
@brianskellenger9344 Жыл бұрын
Thanks, I was reading Algebra the Very Basics and had a question on the first page 😂 good work 👍
@jounoun3600 Жыл бұрын
Thanks for this video. Now i understand this rule perfectly.
@petermcgrandle8298 Жыл бұрын
Thank you very much - one of the things which made me think a lot of Maths was voodoo has now been very well explained.
@DylanLCutshall Жыл бұрын
okay, but what i’d you kept going down. So what’s 3^-1 and 3^-2 etc. Would the division by the base strategy keep working?
@roger727155 жыл бұрын
Hi, your vids are great! Thank You!
@simenhansenbeitesimen7 ай бұрын
My teachet denied this, im so mad
@tchikoumahmoud4665Ай бұрын
Why explain pls why does he deny this
@walterbrownstone80172 күн бұрын
Because the 0th degree of an exponent is not a mathematical operation. It's a definition. The base unit of the function is 1.
@tico6028 Жыл бұрын
Love you for this man
@alexanderbreeding40085 жыл бұрын
This was very helpful to me in understanding this principle while studying for the GMAT. Thank you for making this video!
@neonWHALE0024 жыл бұрын
Interstellar has taught us that the solution to 0^0 is in a black hole
@acktack3578 Жыл бұрын
Good video thanks, it explains the concept clearly and concisely
@juanrodriguez9971 Жыл бұрын
1:32 minutes in and I finally understood why, I guess it's the same as why (-2)^2 isn't the same as -2^2, on both cases there is an invisible multiplication with (-1) so the first one means ((-1)(2))^2 while the second one means (-1)(2)^2 which by order of operations we always do what is inside () first, then the exponents 2nd, and since there is nothing inside the second case we do not multiply (-1)(-1).
@adambakas13 Жыл бұрын
If the reasoning simply doesn't make sense then either the reasoning or the expression of the math needs to change, this is something a whole lot of teachers don't like to hear. Even if a concept works you must find a way to show that it makes sense! If you can't then you can't teach math properly.
@jXd6 жыл бұрын
Ah thanks,... I've read on this and watched other instructional videos but this was the first time it made sense.
@BTS_ARMY1997 Жыл бұрын
Thank you very much. You explained it very well.
@lohasingh9823 жыл бұрын
Thank you sir love ❤️ from India
@hastimak86825 жыл бұрын
It was great . But all the math teachers told us there are many ways to ascertain this subject. Which way we should always use it? which one is better?
@gailmargret233 жыл бұрын
Fantastic. This was making my brain hurt. Thank you for explaining it in a way that didn't make my brain hurt even more.
@justabunga14 жыл бұрын
The video should say any non-zero number raised to the 0 power is always equal to 1. 0^0 is indeterminate, which is useful in calculus to compute limits of indeterminate forms using l’Hopital’s rule.
@minkademko23352 жыл бұрын
Thanks for taking it back in history to how this was originally figured out.
@Ongshimi_Mandu Жыл бұрын
thankful for this video
@JackRumer8 ай бұрын
Thanks, my man
@ricardoblikman26762 жыл бұрын
Honestly I learned my 7 year old son both positive and negative exponents and I did not even have to explain 0 because without power 0 you can not explain 3 ^ -1.
@i_gaurav_kr.17 күн бұрын
Thanks buddy ❤
@Theyadoresharvari._2 ай бұрын
Let the mathematicians lose their mind over that 0, I'm just glad that now I know why anything to the power 0 is one
@donsal.t.17654 жыл бұрын
Thanks once again Jr High!
@aaronrajinthrakumar73907 ай бұрын
what about the rationale behind e.g. y^(1/2) is equal to the square root
@gugulethukheswa4605 Жыл бұрын
Thank you for the explanation
@dayanandt30165 жыл бұрын
please make a video on quantum physics
@jeremy5602 Жыл бұрын
Yo Eric Pyrdz personally produced the music for your video? Amazing! 😂
@jrjr1313jrjrАй бұрын
These definitions work for integer powers, but how do you multiply 1 times 2 to the 1/2 times? or 1 times 2 to the pi times?
@H3VtuxАй бұрын
For Fractional or irrational exponents things get very complicated and there's unfortunately no way I can explain that in a comment section. I would imagine other youtubers have covered this in videos, probably kahn academy.
@serologism5 жыл бұрын
what a nice and simple explanation
@juliapdanderson38915 жыл бұрын
Absolutely brilliant! Thank you very much, thorough and clear 😊
@witchstriker53802 жыл бұрын
Thank you very much, subscribed to you👍😊😊
@manjurhasanchisti22647 ай бұрын
Many thanks.
@alexman974122 жыл бұрын
if y>0, y^x=exp(x ln(y)) then : y^x=exp(0 ln(y))=exp(0)=1 and expo(0)=1 because ln(1)=0 and ln(1)=0 because ln is the unique primitive of 1/x that cancel in 1. and if y
@nicolastelfyr6792 Жыл бұрын
Thank you!
@Kleermaker1000Ай бұрын
The explanation was good, the music bad. :)
@user-jt7vn4pq5c2 жыл бұрын
a^0 = 1 (such that a does not equal to 0) why? proof: a^0 = a^n-n (n-n=0) but a^n-n = a^n/a^n which is equal to 1 clearly(anything divided by itself is equal to 1) hence a^0=1
@Dreamkilled3 ай бұрын
Thank you!!
@quty69364 жыл бұрын
OHHH this makes so much sense!!! THank You so much
@H3Vtux4 жыл бұрын
No problem, I'm glad it helped!
@jonahsousa19863 жыл бұрын
very cool, great explanation
@patricksusulin93353 жыл бұрын
this is truly big brain time.
@captainb.mccrea54804 ай бұрын
Well adding in an ‘invisible 1’ makes zero sense to just add a brand new component, but by that logic, is 0^0 then not 0? Because apparently if there’s always an invisible 1, it would be 1 x 0 = 0. Yet apparently it’s ‘proven’ that 0^0=0? Which I disagree with, if I gestured to the air and said ‘take an object’ there would be no object, because there’s no container, there’s literally nothing there. But once it’s put in some maths equation, apparently people defy real world logic and it becomes something?
@ashishop92332 жыл бұрын
Thanks bro I was finding this and nobody was answering me
@WisdomCalls10 ай бұрын
Thank you. Why books don’t explain this is beyond me
@JJFsixxx2 жыл бұрын
Perfectly said my man
@gamingkids82622 жыл бұрын
When n is not equal to 0, n^0 is 1 BECAUSE: 1. The limit where x approaches 0 in n^x will approach 1 2. n^0 = n^0/x where x is greater than 0. This results in the xth root of n^0, or the xth root of 1, which is always 1 3. n^-0 = 1/n^0 which is 1/1 which is 1. As -0 is 0, n^-0 = n^0 and n^-0 equalled 1 so n^0 is 1.
@AlbertTheGamer-gk7sn6 ай бұрын
0! is not equal to 1 in this scenario.
@mukhtarahmad35323 жыл бұрын
*Amaaaaaaazing Explanation Sir* *Your videos always be Awesome*
@gunterstunter5 жыл бұрын
Great job on this video!
@NiteshBahekar4 жыл бұрын
By these calculations we can 0^0 is coming as infinity and not 0 OR 1 as expected. Even 0^x is coming as infinity.
@BramVanhooydonck Жыл бұрын
Sometimes I like to think dividing by zero practically would mean an object is warped into it's own non-existence. But if you start out with nothing, does the reverse happen? Are things spontaneously created at once?
@H3Vtux Жыл бұрын
I actually did a video on this very topickzbin.info/www/bejne/Z4mzeoqIjcmGg6s
@technoultimategaming29995 жыл бұрын
YESSSS. This IS litteraly what I thought!!! 2^0=? ÷2 2^1=2 ÷2 2^2=4 ÷2 Then did 2^-2= 1/4 So if 2^2 = 2*2 =4 2^1 = 2 2^0 = 1 2^ -1 = 2÷2 Wait no! 2^2 = 1*2*2 2^1= 1*2 2^0=1 2^-1= 1÷2 = 1/2
@kingkirby89605 жыл бұрын
Nice job then!
@karenvickery60705 жыл бұрын
2 / 2 = 1 not 2
@segayanmx44424 жыл бұрын
Hi! Nice demonstration !
@PWR_ADA Жыл бұрын
0^1=0 and to see what 0^0 is you can divide the number you got with the first number so 0÷0=0
@xxJomoxx2 ай бұрын
But doesn't that mean 0 to the power of anything is undefined since 0^2 would be equal to 0^3 devided by zero ?
@H3Vtux2 ай бұрын
No, raising zero to any non zero integer means we're multiplying zero by itself that many times. 0^3=0*0*0 0^0 is the result of two conflicting mathmatical rules n^0=1 0^n=0 So depending on which of those rules we follow we get either 1 or 0 with 0^0...
@kacperzy922 жыл бұрын
pure genius
@thewatcher86573 жыл бұрын
One more: x^y/x^y=1 ----------1 [same numerator and denominator will make 1] also, x^y/x^z = x^(y-z) But here, z=y Therefore, x^y/x^y = x^(y-y) =x^0 ----------2 [y-y=0] Now, x^y/x^y=x^y/x^y From eqn 1 and 2 1=x^0 Hence proved that x^0=1.
@clearlypellucid2 жыл бұрын
What this video really does is explain to me that calling 2^2 "2 squared" is kind of misleading, since what is being done has nothing to do with geometry. If it were about geometry, then 2^2 would be representative of a line segment of length two being made into a square, which would result in 4 units. 2^1 would just result in a line segment, which would be undefined in area, and 2^0 would be a point, also undefined in area. So it's not really about geometry. Geometry just lines up nicely with any exponent higher than 1.
@giorgosg87603 жыл бұрын
a^n/a^n=1, a^n/a^n=a^(n-n)=a^0 => a^0=1 Simple
@RealYukiSan Жыл бұрын
How about 2^(-1) ?
@kandimegahan78444 жыл бұрын
OK. I have 2 comments and a query please: First of all, thank you. Everything about your video is spot on, and I appreciate the presentation. I'm gonna share it with my Facebook community. Someone is sure to be intrigued or at the most, thankful that this little birdy was dropped in their lap. Now for the query, are you sharing this because it (and all my basic math that I thought I never would use anywhere) has something to do with understanding computers and their operations? HINT: PLEASE say NO!
@technoultimategaming29995 жыл бұрын
There is one more thing about 0 I was playing with calculator and saw that tan89.999 and 180/pi aren't that different 57.2957795131... Well I did estemate that tan90 starts with 572957795131.... TanA= sinA/cosA Sin90 = 1 Cos90 = 0 1/0 = 572957795131 Also I said to myself 10 ÷ 2 is how many times can 2 go into 10. So 0 can go into 1 infinite times. But how can a negative number divide negative times? 20/-2 = -10. I kind of get that -20/2 = -10 because 2 can go into neg 20 neg 10 tines
@technoultimategaming29995 жыл бұрын
At this point I don't take the 0 as a number. It does wierd things
@NoahR162010 ай бұрын
Thanks for this. 😅
@renzo9661 Жыл бұрын
How about: Let a>0 ,then a^0=a^1 * a^-1 =a^1/a^1 = 1 I think this is a much simpler way to understand this since if a=0 0^0= 0^1 *0^-1= not defined