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# 1=0.999... ? watch

1. let x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1

or

1/3= 0.333...
3*(1/3)= 1 = 3(0.333...)= 0.999...

2. oh god...

just accept it. for all intents and purposes they are the same thing.
3. (Original post by endeavour)
let x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1
0.9999999=9/10+9/100+9/1000+....
=9(1/10+1/100+1/1000+.......)
in brackets, have sum to infinity of gp first term a=1/10 common ratio r=1/10
using Sum infinity = a/1-r
=1/10/(1-1/10)
=1/10/(9/10)
=1/9
so 0.99999999=9(1/9)=1
4. (Original post by endeavour)
let x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1

or

1/3= 0.333...
3*(1/3)= 1 = 3(0.333...)= 0.999...

Yes.

0.999... = 1.000...

That is the only source of ambiguity in mathematics.
5. Yes but 0.99999..... is a rational number which has infinity of 9's after the decimal point.

So because it is an 'infinite number', we deduce that it is equilant to ∞.

So ∞/∞ = 1
6. (Original post by Vijay1)
Yes but 0.99999..... is a rational number which has infinity of 9's after the decimal point.

So because it is an 'infinite number', we deduce that it is equilant to ∞.

So ∞/∞ = 1
I don't follow what you mean by "we deduce that it is equivalent to ∞".

Also, you cannot say ∞/∞ = 1

What do you define to be infinity? Some infinity's are larger than others, so the ratio of two infinities may not be 1. You cannot simply divide infinity - it is not a number.
7. (Original post by Vijay1)
Yes but 0.99999..... is a rational number which has infinity of 9's after the decimal point.

So because it is an 'infinite number', we deduce that it is equilant to ∞.

So ∞/∞ = 1
0.99999999... is just another way of writing
∑ {i=1 to infinity} 9/(10^(i)) which is the sum to infinity of a gp. This sum has a value we can calculate, it is 1.
8. (Original post by evariste)
0.99999999... is just another way of writing
∑ {i=1 to infinity} 9/(10^(i)) which is the sum to infinity of a gp. This sum has a value we can calculate, it is 1.
Yes, the sum converges to 1. I am not disagreeing with you.
9. You cannot divide infinity because it is not a number.

Of course 3/3 = 1, you're perfoming radicals to finite numbers - infinity is another matter.

By your logic we can say

∞ = x/0

but

∞ = y/0 .... x =/= y

so

∞/∞ = 1 = x/y

but in our assumption, x =/= y.
10. aaaaaah proof by contradiction? glad i don't do P5 ocr!!! lol!
11. What have a let myself in for doing maths at a level???? lawl
12. (Original post by UpliftMof0)
What have a let myself in for doing maths at a level???? lawl
13. 2=1

x=y
x²=xy
x²-y²=xy-y²
(x-y)(x+y)=y(x-y)
(x-y)(x+y)=y(x-y)
x+y=y subsitute x=y
y+y=y
2y=y
therfore 2=1
14. (Original post by S. Tham)
(x-y)(x+y)=y(x-y)
If x=y, then x-y = 0
In the above line, you've divided by x-y, which is division by 0, this is not allowed, hence

2≠1
15. (Original post by Vijay1)
If x=y, then x-y = 0
In the above line, you've divided by x-y, which is division by 0, this is not allowed, hence

2≠1
Indeed.

In fact, the very first mistake was posting this in the knowledgeable realms of the Maths forum. It should only be used in places such as General Chat
16. (Original post by mockel)
Indeed.

In fact, the very first mistake was posting this in the knowledgeable realms of the Maths forum. It should only be used in places such as General Chat
yeh i bet u would fool some people!
17. (Original post by DaveManUK)
yeh i bet u would fool some people!
Yeh thats true, our math teacher once showed us this, so we stared at all the lines and thought to ourselves ( )

Only one person in the whole class spotted it!

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