0.999... (recurring) = 1

[KhyberKhan]

Do you agree?

[khashayar]

I dont care.

[طالب]

Yes.

[Albani_Rahmat_Kabulzada]

No this is not possible.

What makes you think .99999= 1?

1=1.

1.00001 doesn't equal 1 either.

1 is not a specific number. Just replace it with X (=1)

[Albani_Rahmat_Kabulzada]

1 is no doubt a number. It is the first "official" positive number, if a graph is going to infinity. Not counting the . Decimals.

In that case you can replace it with x; x=1

[KhyberKhan]

no

0.999... = x

9.999... = 10x

9x = 9

x=1

[KhyberKhan]

No this is not possible.

What makes you think .99999= 1?

1=1.

1.00001 doesn't equal 1 either.

Store 0.9 as x in a casio and recall it.

tell me what pops up?

[KhyberKhan]

Your being generous now.

X=1

X=\ .999999 then

Consider the following geometric series: 0.9 + 0.09 + 0.009 + ...

The first term is a = 0.9
The common ratio is r = 0.1

The sum of the first n terms is a(1-r^n)/(1-r), the standard formula for the sum of a geometric series.

0.99... recurring, is by definition, the limit of the above expression as n tends to infinity, which exists (since |r|<1) and is equal to a/(1-r).
a/(1-r) = 0.9/(1 - 0.1) = 0.9/0.9 = 1
i.e. 0.99... recurring equals 1.