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Do You Know The 𝗖𝗼𝗿𝗿𝗲𝗰𝘁 𝗔𝗻𝘀𝘄𝗲𝗿 ?
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0.9 bar question is given in NCERT BOOK CLASS 9 WHOSE VALUE IS 1
@@sandeepapandit9573 9th dhang se padha hota to pata hota aapko ....... hai ncert class9 me ye
Yeh ncert cooks in miscellaneous. people who solved intext exercises say it's easy 🤡
@@sandeepapandit9573miscellaneous khol ke dekh liya kar
Bilkul sahi kaha bhai 😅@@rhythmvaishnav7402
Sahi baat hai😂😂@@rhythmvaishnav7402
The logical proof of " 0.999..=1" is that there exists no number between 1 and 0.999...and hence these two are exactly same
Abey tu yaha bhi mila😭
@@Athreya-dc1vy
😭😭😭 Likes ka bhooka
But shouldn't there be a real number between any two numbers on number line?
@@VinitKr086
*Between any two distinct numbers
If there aren't any real numbers between two numbers then those numbers aren't distinct
@@VinitKr086 yes, there should be a real number btwn any two real numbers. Since there is no real number btwn 0.9bar and 1, they must be equal
There are Two explanations:
First one is related to Class 9th NCERT where we use the method to find the rational expression of non terminating repeating numbers
Second one is logical, 0.9bar is equal to 1 because there exists no real number between 0.9bar and 1 and if there exists no real number between two numbers then numbers are equal so 0.9bar is equal to 1
Your whole concept regarding this is wrong
0.99999.... is never 1 it is tending to 1-
And this is the basic concept of limits
But they think they are mathematician...so we can't argue with them 😅😅😅@@sagnikroy3633
@@sagnikroy3633dude did u not watch the video?
@pulsar2977 Yes, I watched, and you better go and study limits first
@@sagnikroy3633that's not really a limit.
Mathematically, `0.9̅` is equivalent to 1. This can be shown by the following reasoning:
Let x = 0.9̅
Then, 10x = 9.9̅
Subtracting the first equation from the second:
*10x - x = 9.9̅ - 0.9̅*
*9x = 9*
*x = 1*
Thus, [0.9̅] = 1
class 9 concept
Dost Mai itna andar kyu gussu .9 is definitely closer to 1 hence if assumed it has to be 1 not 0
@@naruto7034Bhai do jagah bhot andar tak ghusna padta hai , ek maths aur doosra mujhe batane ki zarurat nhi hai
Its actually 0.9999999999..... So multiply by isnt possible you doesn't know it is an infinite digits
If we subtract both equation an (infinite - infinity) indeterminate form appears...so this process is not valid at all
for all practical purposes,0.9 bar=1 is indeed true,but strictly speaking its incorrect
i will explain it in two ways
firstly lets consider L=1-(0.9 bar)
0.9=9/10
0.99=99/100 and so on
(0.9bar=(999.../10^n)) where n is very large
0.9bar=1-(1/10^n) now mostly everyone just applies limit n->infinity and conclude that these are indeed equal,but if we properly use epsilon delta definition,we will see that lhs would only "tend" towards rhs in the long run,but they are not equal
second way is just visualizing this graphically,consider the graph of (0.1)^n,no matter how large the value of n is,this graph will never touch x axis(y=0),hence 0.9bar
Brother it's exactly equals to 1 even by Epsilon delta definition
It is equal to 1 it does not tend to 1. 1-1/10^n tends to 1 as n tends to infinity and hence the "Limit" Is 1. Lim as n tends to infinity of 1-1/10^n is equal to 1. Limit of anything does not "tend" anywhere. It is equal to some value or it does not exist
Okay ... You meant 0.9 bar is less than 1 then by density of real numbers there must exist a real number that is greater than .9 bar and 1 .. can you tell me even a single such real number????
Bro your "n" stuff starts the problem from itself. n should not be a very large number, but maybe ∞. Because bar shows infinite distribution after decimal.
@@sarthaktiwari3357 ever heard of the word adjacent?. Your concept of there exists some real number breaks down when you're taking a number that is in infinity form.. like 0.99999.....
We can also prove it as:
(1/3)×3 = 1 ...(i)
0.3333... × 3 = 0.9999... ...(ii)
But (1/3) = 0.3333...
Therefore, by equations (i) and (ii),
0.9999... = 1
Yes that's what we did in 9th
@@adityagoyal7110 wbse me class 6 me hai
Wrong proof first are you sure than 1/3 is exactly equal to 0.3bar
@@Aaravs21 Yep! 1/3 = 0.3333333.....
@@anamitrakundu56 When I was in class 7th, I just thought about this proof....
[I saw the previous video of this channel also on the same topic]
soch pa rahe ho ? -> nahi -> kyunki hai hi nhi 4:30
WAS EPIC 🤣💀
Ye kya galat time stamp hai bro 10 sec pehle dalo 4:20 is more accurate
Sir, i can't accept that 0.99999.... = 1 because it will become 1 when 0.00000....1 added to 0.999999.... . So their is difference of 0.000....1 between two numbers.
It will be zero only
How did you find 0.00000....001 Is the difference
i think when we are dealing with infinities of any kind the situation becomes more philosophical and less logical
No, logic is still there abundantly but I get your point 👍
4:22 aaj pata chala iss channel ka naam bhannat maths kyu hai dimag bhanna gaya ye sunn k
Sir, the answer is 0
As sir 0.999.... is tending to 1-
Not exactly 1
And using limits, we would get 0
Its not trending to 1. Its exactly 1
4:22 aise to agar domain mera real number k jagah integer ho to 0 = 1 ho jayega kyoki "soch he nahi paa rahe" koi integer jo 0 aur 1 k beech me ho, to usse 0=1 thode he ho jayega?
ye samajh nahi aya.
agar koi doosra number system le liya jaaye, to ho sakta hai 0.99999... aur 1 k beech me koi number exist kare?
converging GP wala sabse aasaan lagta hai samajhne me mujhe to agar reason karna ho to.
lekin, lekin, lekin.... aapka logic se 0.4999999... = 0.5 predict kar liya tha to i guess intuitive ti tha.
thank you.
Sir , Aap ne AOD,limits, functions ki kuchh video hide kr diye h kiyu sir ? Pls reply me
If we go by limit that is if we tend x to 1- and GIF is outside the function then it gives ans 0
Lim. [x] = 0
x approaches 1-
0.9 bar is what? It is x approaching to 1 from left hand side. So if go by this way the ans will be 0.
Then why is lim x-->1-
[x] = 0 ? it should be 1
This limit does not exist, if we take RHL it will give 1 and LHL will give 0.
1- refers to number smaller than 1. Here, we simply don't know whether 0.9 bar is smaller than 1 or not. Then how can you say its GIF is zero?
@@devcoolkolHe said about tending to '1-' not '1'.
You can say that x=0.9999999998 something, but not 0.9bar as 0.9 bar is equal to 1, here it is x->1- i.e. a number less than 1, here 0.9 bar is equal to 1 so we can't tend it to that.
@@devcoolkol i am not saying about limit i am only talking about LHL
Sir by trick 9-0÷9 =1
•
• • true...😊
Just because the difference is really really small, do NOT mean they are equal. GiF me equal ya less than the orginal number aata hai, na ki greater than the orginal number.
Thanks for 150 Subscriber RUclips family 🎉
Check Community post 🎉
Because 0.9 bar is non terminating there will be no other value bw 0.9 bar and 1 so it can be treated as 1 only and GIF of 1 is 1.
Simplest explanation i could think of. Do lmk if incorrect.
Box ki property hoti - x ka gif -1-[x] ke equal hota usse zero aa rha hai. But such problems never come jee jab ayengi tabhi pata chalega.
Another method, Let x = 0.999999....
(1) 🤐
Multipy eqn. (1) by 10 , 😟
Then, 10x = 9.9999...... (2) 🤔
Then Subtract eqn. (1) from(2)
Then we get, 9x=9
So x =1. [H.P.❤❤]
Tnx 💞 to bol do ❤....... { jisko ans. Nhi aata vo 9th dhang se pd leta 😁😆 haha..... }
Acha thnx 💀
0.9 bar = 0.999999999.........
Let X = 0.9999999999...........
Then 10X = 9.9999999999999.........
10X-X=9
9X=9
X=1
So, [0.9 bar ] = [1] = 1
Correct Bro !!
Great bhai
भाई यह तो डेसीमल टु फरैक्सन वाली तकनीक है ।
Aman sir great🎉🎉✅️❤️✅️❤️✅️❤️
If there are 20 buildings in rows , then if we try to find a building in any two buildings we get a building
Except consecutive buildings or one buildings two times itself
So this implies buildings may be consecutive or a same building twice
So my doubt is both number 0.9bar and 1 can be consecutive sir
Please clear doubt.
[0.9]=1 seems to be the mathematically repeating decimal [0.99999...]=1 simple proof of this concept . let x=0.999... Multiply both sides 10. Get ,10x=9.999... Subtract x from new equation 10x-x=9.999...- 0.999... 9x=9 divede 9 both sides. We get x=1. x=0.999... [x]=1. [0.9]=1 hence proof that.
Aise 1-¹ and 1+¹ is also 1 there will be no limits?
Doubt : Sir 0.999999........ aur 1- (Left hand limit of 1) Mei kya difference hai ????? Kya yeh notation same hai ??? 💥💥
0.999999…… -1=0
but this feels so...fishy, i don't know how to say it. its almost like its going against the definition of the box function
it is not, because 1/3*3=1. now 1/3= 0.3(bar) and multiplied by 3 it becomes 0.9(bar). From equation 1, 0.9(bar)=1. So the floor function(box or GIF) gives 1 for 0.9 bar.
@@abhirupkundu2778 i get it, but still, it feels weird to label 0.9 bar as 1 directly *just* because we can't list another real number between it and 1. why do we do that? just because they're very close? then on the scale of integers, why do we treat 1,2,3 as discrete numbers? since in the domain of integers there's nothing between them, isn't 1=2=3 by the same logic?
Your questions sums up your answer. In the real world, there are infinitely many real numbers between two unequal real numbers. But there is no such condition about integers.
However, I do understand how it *feels* weird that 0.9 bar=1. Perhaps it is because we do not grasp the concept of what infinity is.
@@abhirupkundu2778 when you look at 0.9 bar originally it gives the answer as 0 , but when you derive it from some other expression it gives 1 , so I guess the answer 0 is right
@@shantiprakashbihani1420 no it is not. Think logically. 0.9 bar is 0.99999....infinite times. This number is the closest number to 1, and it is so damn close, it is even closer than takimg a limit x->1-. 0.9 bar is actually the closest approximation of 1. Hence in a GIF or floor function,
It is so easy to understand for those people who like infinite series.
Kuch jyada hi pyar se padhate ho ap sir.
2/3 + 1/3 = 1
0.6bar + 0.3 bar = 1
0.9bar = 1
Hence proved😊
Bhai u can't take bar like that
Bhai complex number thodi hai ye kuch bhi
@@trivikram4962 nhi shi hai buss thoda sa ajib sa lag rha hai solution.
@@AdityaKumar-gv4dj sahi nahi hai, galat assumptions hai, 0.9bar can never equal to one it can tend towards one, there's a contradiction with saying that 0.9bar=1
This is not concept of class 9 real numbers but It is of class 11 GIF see this [ ] sign.Don't mix it with real numbers.GIF stands for greatest integer function.
Very Nice 💯 Explanation Thanks 🙏 Sir Ji
Sir kuch din pehlhi yeh sawal mere man mein aya aur dekhiye ajj agaya video,mai ek chiz notice kar raha hoon ki jo mai sochta hu abb abb wo mere sath hone laga hai,kuch powers agaya hai seriously
0.9(bar)=1
Let, x=0.9(bar)
then,X=0.99999......(1)
Multiplication by 10 both sides
Then,10x=0.99999×10
10x=9.99999......(2)
Defferent b/w equation (2)&(1)
10x-x=9.99999.....- 0.99999.....
9x=9
x=9/9
X=1 ✓✓✓
so if 2=2 cuz there is no real nom between them
so if we subtract 2-2 we get zero
but if we subtract 1-0.9 bar we won't get zero . that does means they are not equal and hence its greatest integer will be zero
I salute your knowledgw and explanation 🎉
what about right and left nieghbours of a number
1/3 = 0.3.......
if, 1/3 * 3= 1
then, 0.33.......* 3 =1
So, 0.9999999...... = 1
Agar sir hum natural number ki baat kare toh 2 and 3 ke beech main bhi koi number nahin aata hai so 2= 3 hoga kya
2.1,2.2,2.3.......left the chat😂😂
Perfect knowledge .
ok sir i agree your explanation,thats a very excellent question that i ve ever seen
but i have a doub,t you said if the two numbers are equal so there is no real number between them ,for ex: 2=2
so if i multiply 1 on both sides
2(1)=2(1)
2=2
lhs=rhs
if i multiply 2 on both sides
2(2)=2(2)
4=4
lhs=rhs
similarly: 0.9(bar)=0.1(as u said )
if i multiply 1 on both sides
0.9(bar)(1)=1(1)
0.9=1
lhs =rhs
if i multiply 2 on both sides
0.9(bar)(2)=1(2)
1.9999999999.....................8 =2
1.98 =2 (where 9 have a bar)
so as u said there is no number between two equal number so how it is contain 1.999bar) between 1.98 and 2
sir if u r seeing it sir please make a specific video and explain it please sr
thanks for 69 likes (also reading this )
the entire concept of "bar" is that it never ends, there are infinite 9s after the decimal point, so 8 never comes, it's only 1.999999999999999... all the way through, there is no end where 8 exists
Value is 1^--.slightly less than 1.so greatest integer is zero.
Mast teacher hai ya to 😅😅
Then how
limit x tends to 0- step x = 0
X tends to 0- means there is no number between 0 and 0-
Once explain sir
Sir so from this logic
No real number exist between
0.9999.... And 0.99999.....8 also
So 0.9.....= 0.99999....8= 1
No, because there exists a real number between 0.999... &
0.999...8 and that is 0.000...1(if you subtract these two numbers you will get 0.000...1). So, we can say there exists a real number between 0.999...8 & 0.999... which implies they are not equal .
Therefore, 0.999... = 1
But, 0.999...8 ≠ 0.999...
But, you might think by this logic that 0.999... also doesn't exactly equal to 1. But, there exists no real number between 0.999... and 1 which can be proved by various methods.
In other words, 0.999... is not "almost exactly 1" or "very, very nearly but not quite 1"; rather, 0.999... and "1" are exactly the same number.
Hope that it clears your doubt. 👍🏻
@@aalikh.arora. You are wrong, because by the same logic that 0.9.... = 1,
0.9....8 = 0.9....
The difference between both of these pairs is 0.0.....1 which is actually exactly equal to zero. In fact a.b....c = a.b.... for any fixed sequence of digits for a, b, and c. This is because c lies after the infiniteth decimal place, which means you never really get to c, making the two numbers identical.
@@als2cents679 Thanks for correcting me there 👍🏻
0.00000000...........1 ka differnce jo bahot bahot bahot minor hai jiska aprrox value natural number ayyega
Why are you deleted function and relation old series please sir tell me
mere dimagh mein mai yeh soochata hoon kay
epsillon yah kay dx jaise koi number nahin balke conceptual quantities hotay hain maths aur physics mein, joh zero se jyada aur koi bhi real number se kam hotay hain, inkoh aap relate kar sakatay ho 0.9999.... se
epsillon = dx = 1 - 0.9999....
0.9999999= 1/1 in fraction form
= suppose x= 0.99999999999....... (eq-1)
multiply both sides by 10
10x = 9.99999999 (eq-2)
than subtract (eq-1) from (eq-2)
you will get,
9x=9
x=1
hence proved [0.9999999999999................] = 1😄😄😄😄😄😄😁😁😁😁😅😅😅
class 9 ch-1 RATIONAL NO.S
If we subtract both equation an (infinite - infinity) indeterminate form appears...so this process is not valid at all
0.9bar is equal to 1
Yeh recurring decimal number ka concept west bengal board me 6th standard ke syllabus me hai.
Infinite series se bhi iska proof hai.
But sir aap jo explanation diya woh bas ek intutive idea mathematically proof also important here
.999------ is not an exact number but 1 is an exact
number.How can you represent .999--------- on number line. When you will represent it on number line,you will never reach 1 in your whole life.Then,how can they be equal.
Add .999-------+.999--- .what
will be the sum.Please,try
@@ashtavakraphysicsclasses1213
This is happen due to infinity
I am with you
[0.1bar] 4:30
0.9999... = x
10x = 9.9999...
10x-x = 9
9x = 9
x = 1
This is not concept of class 9 real numbers but It is of class 11 GIF see this [ ] sign.Don't mix it with real numbers.GIF stands for greatest integer function.
Nice
Let, x = 0.9999... ----- (i)
On multiplying both sides of Equn. (i) by 10
10x = 9.9999... ----- (ii)
Equn. (ii) - Equn. (i)
10x - x = 9.9999... - 0.9999...
=> 9x = 9
=> x = 1
Hence proved.
It is humble request to you Sir to discuss some tough arithmatic problems as well.
Just because infinity is not defined, while proving we take 1 extra 9 beacuse of infinity.
Hello Big Guduji, from which original verb you've found da word "explaination' as noun ?
Isn't it "explanation"?
😱😱 point of view!
I'm just asking whether 0.000000.......1 will not be there between 0.9bar and 1?
Sir what about lim[x] as x--->1 where[.] is GIF
x=•99999----
Donot muliply by 10 on both sides
But add 10 times,then show,x is 1.Multiplying by 10 or adding 10 times must give same result.
Please reply.
Whole life will spend in answeing.
there are infinitely many 9s in 0.9999..., and the moment you start comparing infinities, you will be in a dilemma :) I mean saying that 0.99999... and 1 to be equal, according to me, is like saying infinity=infinity+1, and again you have compared two infinities:) i may be wrong so pls correct me!
According to me you are incorrect. First of all infinities are not comparable and not relevant to this as they are just a different topic. Here, we say that if two numbers are same there will be no numbers between them. And 0.9 bar and 1 have no number between them. This has no connection with infinities
@@digitalogy2807 1. I just told the same thing, that you can't compare infinites or else you will be in a trap.
2. how many 9s are there in 0.9"bar"? too many, right? I mean how can you prove me that there are no numbers between 0.999... and 1, by just saying so? You can not "count" how many 9s are there in 0.9"bar", which somewhat relates to uncountability of digits in infinity, at the end infinity is just a depiction of large quantity, not a number! Although I agree that infinity is a different topic, but why not relate here... pls tell where i am wrong :)
that's exactly my thought
No, 0.9999... is not infinity. It has absolute value of 1. Only that infinite number of 9's can be used after decimal point to express 1.
Why not it be considered as the largest number between 0 and 1? You see there are two possibilities when there is no real number between two real numbers:
1. The two are same
2. This case
I like GP explanation more because if this number is a representation of that infinite GP, then its OK.
Sir 0.9999...... or 1 ke bich me 0.0000000....1 hota hai pls sir mera confusen dur karo.... ye number to bich me hai ,sir your support 🤓
0.9999.. = (0.33333..) x 3
[Let x = 0.9999..]
x = 1/3 x 3
[3 cancels out]
[x = 1 ] ✓
if we assum infinity as a constant then there is a number we gets when we subtract 1 and 0.9 bar
that is
1-0.9bar = 10 ki power - infinity
1-0.9bar = 10^(-)infinity
1 should be the least upper bound of 0.999...
Here we take the greatest integer function of 0.999....
Since 1 is the lea least upper bound of 0.9999... which is integer also .
So Great integer function of 0.9999... is 1
Agar ye explanation maan liya jaye to phir GIF ka Har integral points per limit exist karega, aur wo continues bhi hoga.
Gp method is wrong.When u take the lim n-> inf 1-1/10^n u will end up with same expression,i.e,0.9bar
With due respect sir ,if you have time ,please elaborate it for weak students😊
I did it through GP and I didn't found anything abnormal in it
10:25 ya hi satya hai was amazing
This is valid sol. That 1 write is 0.99999
Now 099999=0.9+0.09+0.009+0.0009+0.00009
Thus common ratio is o.1
Then 0.9/1-01=1that's it
Check the derivation of this formula
Sir tab aap bataiye ki 1 ke just adjacent aur usse kam konsi value hai ?
0.9bar8
@@shailnair2243 well you are not allowed to use bar as that.
@@shailnair2243 also 0.9 bar 8 is same as 0.9 bar
4:20
Yes
Your no. 0.9999999 . . . . . .
Bigger than above is
0.9999999 . . . . . . ' .'
Sir, please 😟 make a video on the question :
Q. The equation (x ^ 2 + x + 1) ^ 2 + 1 = (x ^ 2 + x + 1)(x ^ 2 - x - 5) for x \in (- 2, 3) will have number of solutions,
(1) 1. (2) 2. (3) 3. (4)Zero.
Sir I waiting for your video. 🙂🙂🙂🙂🙂
No any number always exist in between two nearby adjacent number
Hence proved 0=infinite
This is just a logic.
.9999999 =1
.9999999=.9999998
.9999998=.9999997
.9999997=.9999996
.....
..................
........
.89999999=.9
......
....
......
0= infinite
Salute bro...
Great thinking 🙏🏻
Make it in simple way
The given expression
(9-0)/9
=9/9
=1
Sir when we say x tends to 1- then is it 0.9 bar or a different number?
It is 0.9 bar bro
@@indianinformer1630No it is a numbet less than 1 not 0.9 bar as 0.9 bar=1
In my opinion, limit of 1- contain the values which are almost equal to 1 and which are less then 1.
For example, 0.99...8 or 0.99...89 or 0.99...7 etc.
Not 0.99 bar because it is 1 that sir proved.
( even 0.9 is not 1- but we assume it for easily understand GIF function in limit)
So the GIF of 1- = 0 but GIF of 0.99 bar = 1
I hope my logic is correct
@@AdityaKumar-gv4dj it is the only real no. That approaches to 1 very very close and just at left side of 1 on the number line
0.999999....
Otherwise 0.999....9 should be terminated for that no which says this no. Is not at just left neighborhood of 1
Not equals to 1
A good reason for you
If
0.9999....=1
Firstly see this(2*0.9=1.8 ,2*0.99=1.98,2*0.999=1.998, 2*0.9999=1.9998
General 2*0.99... upto n times =1.99999...8 (n-1) times 9
2*0.99999..=(2*10^n -2)/10^n-1
Now n tends to infinite
Then 2*0.99999...= (20000000....-2)/100.....) =inf/inf = indeterminate form
But as per your assumption
0.999999....=1
2*(0.9999...9)=2
Hence inf/inf =2 wow magic
If two stone is placed just one after one then there is no stone between them. Is that mean two stone is in same position??
No, but we can surely add another stone in between those 2 stones
The stones are not 2 but 1
@@C.I.D_Inspector_PJ_Mask no I mean if two stones touches themselves then?
Sir toh fir kisi function ki range me open 1 or closed one kyu hi likhte hai?
No Namo sir is harmed here😂😂😂
0.99999999 = 1 ( Indian mathematician ( Sridharacharya book 760 C E ) Proved
Using infinite series, we can prove it easily..
Sir if we take two consecutive number then no number lie between it the given number we can say tends to 1 from lhl so its gif should be 1
I agree with your explanation. But can you explain that
1-0.9=0.1
1-0.99=0.01
1-0.999=0.001
1-0.9999999999=0.0000000001
So it’s not matter how many 9 your consider after decimal but if you substrate it from 1 you will always get a 1 after so many zeros. So it will never be absolute zero. So both are not equal
Bro, according to you 0.9bar < 1
Ok you are indeed correct
1-0.9=0.1
1-0.99=0.01
......
But first say when 1 comes at end , when the number is finite i.e.(0.9,0.99.0.999...)
But in 0.9bar case , the nine is repeated infinitely
So , we cannot say that 1 comes at end , if comes then it contradicts the fact that 0.9bar is not repeating infinitely
Sir i would like to question your logic by
Agr 0.9bar and 1 ke bich mein koi real no nhi hai toh 0.9 bar=1 ok
But then if 0.9bar=1 so 0.9999999999.......................at last 8 and 1 ke bich mein kon sa real no hai
Kyuki 0.9bar and 1 equal hai
Agr nhi hai toh kya ye no. Bhi 1 ke equal hoga aise toh hae decimal 1 ke equal hoga
Spelling of explanation is explaination
Main jitne bhi Sir se mila hu ajtak Aman Sir mera favourite Sir hain
The simplest explanation:
What is 1÷3 if we use decimal point?
1/3
=0.3 + (0.1/3)
=0.3 + 0.03 + (0.01/3)
=0.3 + 0.03 + 0.003 + (0.001/3)
=0.3 + 0.03 + 0.003 + 0.0003 + (0.0001/3)
= 0.3333 + 0.0001/3
You can go on infinitely....
Now if you multiply this with 3, you get
[0.3333+(0.0001/3)] × 3
=0.9999+0.0001(=1=(1/3)×3))
So, if you want to express 0.9999+0.0001 using only nine, you can do so by using
0.0001= 0.00009+0.00001
Now, 0.9999+0.0001
= 0.9999+0.00009+0.00001 as above
=0.99999+ 0.00001
= 0.999999+0.000001
=0.9999999+0.0000001
=0.99999999+0.00000001
=0.99999999... =1
Putting it in anothe way,
1=0.9 +( 0.1)
= 0.9 +( 0.09+0.01)
=0.99+(0.01)
=0.99+(0.009+0.001)
=0.999+(0.001)
=0.999+(0.0009+0.0001)
=0.9999+(0.0001)
= 0.9999...=1
This bar expression implies that there is always a remaining part having 1 in the form of 0.1, 0.001, 0.0001...
God of Mathematics ❤❤❤
❤❤
4:29 0.1+0.9=1
Because 0.9999999999.... is approximately equal to 1
There exists infinite number between o.9 bar and 1 so how it is possible?
My question is we know that there exists no real no. Between 0.9bar and 1.0 but it's like saying that one thing is equal to another thing because there's nothing in between but those two things could be adjacent to each other. So 0.9999... exist somewhere on the number line and 1.0000 is the next value on the number line but we can't say that both are equal. The definition that there ALWAYS exist some real no. Between 2 real numbers Is not valid when we are taking no. In the form of infinity like 0.99999......
Number line is continuous, not discrete to day things are adhacent
0.9999••• infinity ki tarah hai, aur infinity to koi number nahi hota, to ham use number kaise consider kare?
Awesome explanation. Very informative...
0.9 bar is not equal to 1 because there is a number between 0.9 bar and 1 is 0.0bar1
0•9bar=0•99999,,,,,,, that is infinitely tends to 1