This is very interesting. Many of us know it.
1=0.9999...........
Don't worry. Everything is right about it.
For example 1/3 = 0.333333...........
ie 3 * 0.333333...... = 1 (if x/y = z, then yz = x)
ie 0.99999........ = 1 (since 3*0.3333..... = 0.9999........)
The proof goes like this
let x= 0.9999........
hence 10x = 9.9999........ (multiplying both sides by 10)
subtracting the two equations we get,
10x - x = 9.9999........ - 0.9999.........
ie 9x = 9
ie x = 1
ie 0.9999....... = 1 ( as x = 0.9999.... & x = 1)
Hence proved
PS Dont try to find any mistake in the proof because there isn't any.
Please let me know if you are interested in such posts.
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22 comments:
Yes Sir, would like to see more of such funny proof's & some tips on Vedic mathematics as well...i can read them & try to learn some maths :)where's ur book on Vedic mathematics?? Only 2 chaps kya?? Is it taking so much time???
No contradictory opinion/ comment on this from my side :)
ya that is too great to read for people like who are illliterate in maths!!!!!!!!!!!! lol!!
hey dat was nice.....really hope to get more posts on this subject !
thx for the responses
haan re..point hai... ;o) tu toh mastermind hai re... koi tera galti nikalhi nahi sakta.. kitna bhi koshish kare log...
hmmmm hari I must say your friends expect right decision and view from ur side... so you have to better be careful all the time as expectations are high frm u...all the best and God bless
thx a lot sonica
take this one :
a = b --( Statement 1)
lets subtract (a + b) / 2 from both sides
a - (a + b)/2 = b - (a + b)/2
lets square both sides
a^2 - 2 * a * (a + b)/2 + (a + b)/2 ^2 = b^2 - 2 * b * (a + b)/2 + (a + b)/2 ^2
simplifying ..
a^2 - a(a + b) = b^2 - b(a + b)
mark this as statement 2.
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Now, lets put a = 5 and b = 3 in statement 2.
LHS = -15
RHS = -15
Hence statement 2 is correct. Means statement 1 also has to be correct. i.e. 5 = 3. Inst it ?
Just try putting any two numbers as a and b, you'll find them equal. Interesting .. right ?
this proof is based on assumption tht second statement is true based on the assumption made in statement 1. Hence statement 1 is true. Even if statement 1 is false statement 2 may be true.
Example assume 3 = -3
squaring both sides we get 9 = 9 which is a true statement but tht doesnt make the assumption true.
As P implies q is true even when p is false and q is true.
I hope i am right. Please correct me
PS My maths will surely not be as good as urs.
Thx for ur interest in my blog. Hope u will continue showing the interest
write down the proof upside down. start with result which u got in statement 2. still statement 1 will hold true resulting any number equal to any other number.
if we write the proof upside down then we r taking square root on both sides and when we do tht it will be +\- on RHS
if a^2= b^2 tht means either a = b or a = -b but not both.
It cannot be like 3^2 = (-3)^2 hence taking square root on both sides we get
3 = -3.
it actually should be 3 = +/- (-3)
ie 3= -3 or 3 = - (-3)
out of which second one is true and not the first
dont you also know tht its interesting but not true
Its very difficult to prove it wrong. really interesting.
u guessed the answer in between ... but you didn't pay attention ;)
the problem with the proof is : you are actually doing it from statement 2 to statement 1 so you have to validate each step that way only.
At one step, when you take square root of both sides, you have two options to consider .. plus and minus. and here we are assuming only one and leaving other. This injects inconsistency. hence the proof is wrong. if you consider both plus and minus roots, then you need to take modulus of both sides, which will keep results proper and show the exact problem with the proof.
Actually, if you see the proof carefully and understand its meaning: You are starting with two numbers and you are subtracting their average from both sides. So on one side you get a positive number and on other side you get minus of the same number. They become equal when you square them.
Which makes 3 = 5 .. or any number equal to any other number :)
Interesting one .. right ?
yes sir it is very interesting
looking forward for many more of such mind boggling things
hey buddy .. don't call me Sir. I am just a noob blogger.
If you like, feel free to visit my blog हम बोलेगा तो बोलोगे के बोलता है |
i am not convinced with this proof...according to me you are deriving the value of 1 from 0.9999...you are not equating 1 with 0.9999
@arun
there is nothing wrong in the proof
i didnt get what u r saying
what i am saying is you already have a number..you are massaging it to arrive at another number
already have a number meaning.
U mean x =0.9999....
and then i proved x = 1. I didnt make any wrong step
hey hari the concept of fun with maths u started in class is really awesome.really hope 2 see more fundas......
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