Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**goddess****Member**- Registered: 2005-03-12
- Posts: 4

it is thought that :

x=0.9...

10x=9.9...

9x=9

so

x=1

but if you do 1+1 you get 2 and with 1+0.9 you get 1.9...

Offline

**goddess****Member**- Registered: 2005-03-12
- Posts: 4

it had to come up some time

please help

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,657

Welcome, Goddess.

Well, I guess that is the thing about mathematics. It's gotta work all the time!

I suppose you read our page on 9 Recurring

Well, let us try with your variation: **Does 1 + 0.999... = 2** ?

Let X = 0.999...

So, we are asking: Does 1+X = 2 ??

Let's start with: 1+X = 1.999...

Multiply by 10: 10(1+X) = 10(1.999...)

Or: 10+10X = 19.999...

Subtract X from each side to give us: 10 + 9X = 19.999... - X

but we know that X is 0.999..., so: 10 + 9X = 19.999... - 0.999...

or: 10 + 9X = 19

or: 9X = 19-10 = 9

or: X = 9/9 = 1

So, X is equal to 1 and also equal to 0.999... (because we said so at the top)

Therefore 0.999... = 1

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**goddess****Member**- Registered: 2005-03-12
- Posts: 4

thank you

Offline

Pages: **1**