*don't*. The civilized world bases its numerical system on groups of ten:

1 2 3 4 5 6 7 8 9 10

Using this method, 0.9 = 9/10, of course. But what if a civilization decided to base its numerical system on groups of what we call "twelve"? It might look something like

*this*:

1 2 3 4 5 6 7 8 9 A B 10

"10", to this hypothetical civilization, would be the equivalent to our "twelve".

.6 would be equal to 1/2.

What if a civilization based their numerical system on groups of what we call "five"? It might look something like this:

1 2 3 4 10

Their .4 would be the equivalent to our .8, or 8/10.

In conclusion, 0.999...=1 just because

*we*decided to assign "9", the ninth number, as our highest valued digit? In the numeric system of the first of the two suggested hypothetical civilizations,

*their*.B is equivalent to

*our*11/12.

*Their*.B is closer to 1 than

*our*.9, or 9/10.

**If**, because when using the

*you*think that 0.999...=1, then you*must*also agree that 0.888...=1*second*suggested hypothetical civilization's numeric system, that's

*the best you've got*.

That's why

*I*say, "0.999...

*does not*equal 1, no matter

*how hard*it tries".