Is 1 bigger than 0.99999...... or they are equal?

Question

Here is question which always disturbs me. Could somebody help me?

Is 1 bigger than 0.99999...... or they are equal?

Thanks for your help.

score 3 · Accepted Answer · answered Apr 17 '13 at 02:33

3

They are equal. Suppose not. Then $|1-0.\dot{9}|=c>0$. However, $|1-0.\dot{9}|$ is less than any given positive number, this is not possible as $c$ is a fixed positive number.

answered Apr 17 '13 at 02:33

Easy

4,485

score 2 · Answer 2 · answered Apr 17 '13 at 02:32

2

Hint: $10 \cdot 0.(9) = 9.(9)$

answered Apr 17 '13 at 02:32

gukoff

1,500

Is 1 bigger than 0.99999...... or they are equal?

2 Answers2

Linked