Does .999 repeating equal 1?

[Hauldren Collider]

Does it? I'm pretty sure no part of .999_ = 1 is unsolved

[Kidlicious]

This whole thread is a joke, right?

[loinburger]

Does it? I'm pretty sure no part of .999_ = 1 is unsolved

It's unsolved for those who flunked calculus

[Vanguard]

Okay, my final words on this subject, which is honestly kind of boring.

Let's go back to Skyfish's proof and my criticism of it:

Skyfish's proof:

Let x = 0.999...

Then 10x = 9.999...

So 10x - x = 9x = 9.999... - 0.999... = 9.

Since 9x = 9, we have that x = 1.

Therefore, 0.999... = 1.

My reply:

Unfortunately, this is self-contradictory. If .999.... = 1, then you can substitute 1 for .999... at any point and the results should be the same. But if you substitute it in the third line:

10x - x = 9x = 9.999... - 1

then the result is not 9, it is 8.999...

This is not a trivial objection that you can wave off by saying "So what?". I have completely invalidated the proof.

Remember, if .999... = 1, I can substitute 1 for .999... at any point in Skyfish's proof. Because they are equal. I don't have to be consistent; I can put a .999... in one place but not anywhere else. Because they are equal. And no matter where I perform this substitution, the proof should still work.

But when I actually do this in one location in the proof, the equation no longer appears to work. And the only way to get it to work is to assume that .999... = 1. Which means the whole proof is a circle jerk----- 999.... = 1, therefore .999... = 1. Which is meaningless. The proof fails.

What should we take away from this? Well, don't be confused. The fact that Skyfish has not proven that .999... = 1 does not mean that .999... is not equal to 1. He just has not proven it.

But we should also note that legitimate proof is extremely difficult in this case. Rigorously proving that one number is equal to another number in the same number system is probably impossible, since it contravenes the basic concept of equivalence. Which is kind of hard to get around when doing proofs. But none the less, .999.... does appear to be equal to 1. So what do we do?

The solution is not more invalid proofs. The solution is to define .999... as being equal to 1. Because it is not rigorously proven, but is still true.

[loinburger]

Likewise, Hercules never catches the tortoise in Zeno's paradox, because apparently we're dismissing all of calculus

[Elok]

Since this thread is all about the irrelevant, I feel no qualms about pointing out that I think it was Achilles, not Hercules. And you'll probably DanS me, and it'll serve me right.

[loinburger]

I am slain

[loinburger]

However, I'd like to point out that the Wikipedia article uses a bus for the dichotomy paradox, which I'm pretty sure is not Zeno's original wording

[Hauldren Collider]

Likewise, Hercules never catches the tortoise in Zeno's paradox, because apparently we're dismissing all of calculus

Math should have ended with long division. **** this algebra ****.

[DaShi]

Advanced math is part of Obama's plan to indoctrinate our children into liberalism.

[loinburger]

It was all downhill once they came up with the zero

[giblets]

Likewise, Hercules never catches the tortoise in Zeno's paradox, because apparently we're dismissing all of calculus

So time and motion are now illusions?

[giblets]

Advanced math is part of Obama's plan to indoctrinate our children into liberalism.

Duh. Equality is against nature. Ergo .999... can't equal 1. Case dismissed.

[DaShi]

Affirmative action for numbers!

[loinburger]

So time and motion are now illusions?

We need to make a few sacrifices in our embrace of facile post-modernism