0.999....=1

[Teeqoz]

 

Platina said:
Math doesn't work that way

though it does look neat

[1/9]*9 = 1, not 0.999...                                     

Actually math does work that way. 

And 1/9*9=1=0.999...

1/9=0.111... you agree on this, right?

and 0.111...*9=0.999... you agree on this as well, right?

Now, since 0.111... = 1/9, and 0.111....*9=0.999... then 0.999....=1

Peh said:

Teeqoz said:

Yes I can, because I've defined x = 0.999...

 No you can't. Your replacement changes the whole equation. That's not how algebra works. I cannot randomly replace numbers out of the blue.

Faelco explained it pretty well here, so I'll just give you his reply to someone questioning the same thing.

Faelco said:

Davman said:
Guys i don't know good english but i am mathematician and you cannot replace a number with an unknown number you are looking. And in second example you made mistake in basic math execution.

The "If x=0.999999..." or equivalent is basically the first sentence of any mathematical problem or demonstration. Of course you can replace your "0.999999999..." by x.