Did you all know...?

Question

Did you know that the number .999... (aka .999 continued) is equal to 1?
I'm speaking of this as a matter of fact. The symbol .999... and 1 represent the same value.
Here are a couple of simple ways to establish this.
Subtract .999... from 1. You get 0.000...
Add .999... to .999.... Do it again. And again, and again. You'll notice that each time you do, the value of your sum increases by exactly 1.
Here's another way of looking at it. There is no number, no matter how small, that you can add to .999... that would make it 1. Any number you add will result in a sum of more than 1.
Keep in mind that there is no such number as .000...1. The idea of the whole "repeating" denotation is that the 0's continue on that way forever; placing a 1 on the end is a contradiction in terms.
I love a good argument, so please, tell me if I'm wrong :)

If your curious as to why I placed this in the religion category, it's that the religion category seems to attract ignoramii who will die by their knee-jerk reaction, no matter how silly or uninformed it is. Like I said, I like to argue.

Also, if you really don't know the difference between .999 and .999..., here it is. The ellipses indicate that this is a continuing series of 9's that goes on infinitely. .999 and .999... are not the same.

Gwen H., you're a ditz. I am not proposing that these are "roughly" equal and therefore equal; I'm saying that different symbols represent the same value, just as 1.000... is the same as 1.

Magley, you're wrong too. You can't have an infinitely repeating series of 9's "with an 8 on the end". Consider that possibility, and see if you can figure out why not. Do you know what it means to have an infinitely repeating series of numbers?

Common_Sense_Don't_Hurt - You're a "degreed mathematician," eh? Well, .333... is equivalent to 1/3, and .999... is equivalent to 3*.333.... Since your school couldn't hammer into your skull that 1=3/3, you might want to try selling your diploma back. It isn't doing you much good.

Common_Sense...
Slow down a little.
So you're saying that .999... is different from 3/3?
If 1/3 = .333..., and 3 * .333 = .999..., how is .999... different from 3/3?
Pray enlighten us humble ignorant non-mathmeticians. Incidentally, before you claim a consensus of authority on your side, you might want to do a teeny bit of internet research. This is old news, friend.

Okay, I rest my case here. Common sense, if you don't think that .333... is actually equal to 1/3, but is only close, then this is pointless. I can't argue against a made-up decimal system.

Answer 1

Yes, I did know that.
I'm surprised that people don't understand your use of ellipses. I thought you explained it fairly well.