To find the difference between two numbers, you subtract, right?

So if we take .999 repeating to infinity and subtract it from 1, we get .000 repeating to infinity. The theoretical .01 on the "end" of the chain never appears. Hence, we find that the difference between .999~ and 1 is .000~, or simply 0. Therefore, 1 and .999~ are the same number.

.999~=1

Let x = 0.999999999999~

10x = 9.999999999999~

Subtract (x) from 10x:

10x = 9.99999999~

-x = .99999999~

Which means...

9x = 9

Which means... x = 1

So, therefore, 0.999999~ is the same number as 1.

So if we take .999 repeating to infinity and subtract it from 1, we get .000 repeating to infinity. The theoretical .01 on the "end" of the chain never appears. Hence, we find that the difference between .999~ and 1 is .000~, or simply 0. Therefore, 1 and .999~ are the same number.

.999~=1

**OR**Let x = 0.999999999999~

10x = 9.999999999999~

Subtract (x) from 10x:

10x = 9.99999999~

-x = .99999999~

Which means...

9x = 9

Which means... x = 1

So, therefore, 0.999999~ is the same number as 1.

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