a = 9.999999...
10a = 99.999999...
10a - a = 90
9a = 90
a = 10

yeahhh, What's wrong with mathematical proof ?

ehehe:) this brought back the GCSE years of my life:) pure hell :) its been so long i have not been involved with numbers... however im gone take a wild guess. could it be ;

a = 9.999999...
10a = 99.999999...
10a - a = 90
9a = 90
a = 10

yeahhh, What's wrong with mathematical proof ?

in the big red part, you have taken 'a' away from 10a, yet 'a' is anonymous... and at the next stage the result is 9a.

i dont have a clue :) but just made a wild guess like i said 'long time no maths' :) {mind u i did get an A for maths at gcse's :D but about 6 years ago :D)




actually looking at it again, i think i was wrong, it could of been simplified :)


for god sake, can u tell me the answer plzzzzzz !

I agree with Naz
The variable "a" is supposed to be a decimal number that is "exactly" equal to the infinite serie 9,999.. which in this case it isnt "exact" but an approximation.
Thus, when you substract a finite element from an infinite serie, the remainder is again an infinite serie, not a decimal.

That's the flaw.

OK..
Solutıon
0.99999=1
1.99999=2
2.99999=3
2.99999=4
and so on...
10 = 9.99999

reference=
http://rinkworks.com/brainfood/p/math2.shtml

i still didnt get the logic :D anyways i dont even like maths what am i doing here :D

Naz

It says there's no flaw in the proof.
9,999...=10

so basically they just round up the re-occuring decimal number yeah ?? :)

u know what good job i dont do numerical subjects :D i hate numbers :D

Yep, you're right

10a - a = 90

a(10-1)=9a=9*9.999999...<90 !!!!!!!!!!!!!!

I understand how you can find it.. so ,the first thing to do 9*9.99999
my calculator said=:)9*9.9999999...=89.99999999
In other words =89.999999..=90
Actually,there are several things that make this mathematics proof?
first of all ,why is 0.9999=1 ?

1/3 = 0.3r
2/3 = 0.6r
3/3 =? 0.9r

Is that what you mean?
But in my opinion 0.3r , 0.6r and 0.9r are just conceptional expressions.
Therefore it's a matter of interpretation if you say 0.9r tends to 1 or 0.9r is equal to 1.
0.9r tends to 1

Why does 0.9999... = 1 ?
The first thing to realize about the system of notation that we use (decimal notation) is that things like the number 357.9 really mean "3*100 + 5*10 + 7*1 + 9/10". So whenever you write a number in decimal notation and it has more than one digit, you're really implying a sum.

So in modern mathematics, the string of symbols 0.9999... = 1 is understood to mean "the infinite sum 9/10 + 9/100 + 9/1000 + ...". This in turn is shorthand for "the limit of the sequence of numbers

9/10,
9/10 + 9/100,
9/10 + 9/100 + 9/1000,
...."


One can show that this limit is 9/10 + 9/100 + 9/1000 ... using Analysis, and a proof really isn't all that hard (we all believe it intuitively anyway); a reference can be found in any of the Analysis texts referenced at the end of this message. Then all we have left to do is show that this sum really does equal 1:

Proof: 0.9999... = Sum 9/10^n
(n=1 -> Infinity)

= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)

= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)

= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)

= .9/(9/10)

= 1


Not formal enough? In that case you need to go back to the construction of the number system. After you have constructed the reals (Cauchy sequences are well suited for this case, see [Shapiro75]), you can indeed verify that the preceding proof correctly shows

lim_(m --> oo) sum_(n = 1)^m (9)/(10^n) = 1
0.9999... = 1

Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.


Another informal argument is to notice that all periodic numbers such as 0.9999... = 9/9 = 1 are equal to the digits in the period divided by as many nines as there are in the period. Applying the same argument to 0.46464646... gives us = 46/99.

References
R.V. Churchill and J.W. Brown. Complex Variables and Applications. 0.9999... = 1 ed., McGraw-Hill, 1990.

E. Hewitt and K. Stromberg. Real and Abstract Analysis. Springer-Verlag, Berlin, 1965.

W. Rudin. Principles of Mathematical Analysis. McGraw-Hill, 1976.

L. Shapiro. Introduction to Abstract Algebra. McGraw-Hill, 1975.


--------------------------------------------------------------------------------

From the Dr. Math archives:
How can .999999.... equal 1?
3(1/3) = 3(.3333...) = .9999... = 1
Getting 0.99999...
The Infamous .999... = 1
Other Ways to See That 0.999... = 1
What is 0.999... + 0.999...?
reference=
http://mathforum.org/dr.math/faq/faq.0.9999.html

With other words: If nothing is in between, it's equal.

oh my god :D what on earth r u lot talking about :D

u not what this whole mathematical logic thing seems so hard to me, however im so proud of u lot because u lot are so smart with all these numbers, but most importantly you are so good at expressing yourselves in other languages. go on boys :)

hey naz, back again?? yeahhh where have u been 4 such a long time? i can't believe it. is everything ok with u? i agree with ur first message here: 10a-a=9a. u are amazing, i am glad u noticed it and of course 90a is wrong. i'm proud of u. i always thought we girls are not as clever as boys in maths. u proved me wrong.
öptümmmmmm...

. i always thought we girls are not as clever as boys in maths. ...
actually,the best way to begin to understand the situation is statistics.I think , girls are more clever than boys..

I think , girls are more clever than boys..

exactly, I agree with u.

a = 9.999999...
10a = 99.999999...
10a - a = 90
9a = 90
a = 10
i study maths n there is no worng here! wait..

OK..
Solutıon
0.99999=1
1.99999=2
2.99999=3
2.99999=4
and so on...
10 = 9.99999 izmir ksk u wrote that 2.99999=3 and look at again 2.99999=4 therefore u are thinkin that 3=4 right? first mistake! also no1 tells 0.99999=1. if u asked me reason? well because of we accept 1. when we solve a problem in maths we dont wanna affor with mix numbers clear? i dont know some1 took limits another page but pay attention a or x solution all number! maybe i cant see wrong now in your problem izmirksk altought i dont think so.
take care yourself at here c u then

2.99999999=3 ok...

3.99999999=4



0.999999=1 (you must learn this)
reference=
http://mathforum.org/dr.math/faq/faq.0.9999.html

just to prove how clever girls can be...:surrender

I'd like to file a complaint..:) clever girls aren't available..why?:):)

Three quarters of the area of the rectangle has been shaded. What is the value of x ? (NB The diagram is not to scale.)

son soru klas bir soru değil mi:)

The area of the rectangle is 6 ×8 = 48 square units, so the unshaded area is
1/4 *48= 12 square units. Therefore

(1/2*x*2)+(1/2*(6-x)*8)=12 that is , x + 24 - 4 x = 12, so x=4.

You are told that 30 pupils have 25 different birthdays between them. What is the largest number of these pupils who could share the same birthday?