Does .999 repeating equal 1?

[onodera]

In what programming language would the statement:
".999 repeating" == 1
be true?

In computers, .999 repeating is not the same as 1.

In the magical world of unemployed mathematicians and underpaid math teachers and completely useless academia, your results may vary.

I'm actually supremely annoyed by the futility of math properties such as this. It's one reason I gravitate towards computers with binary truths and literal comparisons.

Edit: That thread is a decade old...

Asher, you little troll. There's no way to express 0.(9) as a floating point number. Hell, you can't express even 0.9 as a floating point number.
Actually, it's possible to express 0.(9) as a floating point number: 1.0e0

[Dinner]

Onodera, how big were the protests in Moscow this weekend? They made all the news here in America but I wanted to hear it straight from an actual Muscovite.

[onodera]

Onodera, how big were the protests in Moscow this weekend? They made all the news here in America but I wanted to hear it straight from an actual Muscovite.

This weekend? Rather small. Perhaps they were showing earlier protests?

[Jaguar]

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.

Incorrect. If x = 0.999... I can substitute x for 0.999... at any point in the proof and it should still work.

I choose to use that substitution at your last line: "x = 1."

After substitution it reads "0.999... = 1." That shows that your proof relies on the same property it was trying to prove. I have completely invalidated it.

[KrazyHorse]

[MikeH]

[Vanguard]

Incorrect. If x = 0.999... I can substitute x for 0.999... at any point in the proof and it should still work.

I choose to use that substitution at your last line: "x = 1."

After substitution it reads "0.999... = 1." That shows that your proof relies on the same property it was trying to prove. I have completely invalidated it.

No. You have invalidated Skyfish's proof. Since the proofs ARE EQUAL.

Thanks for the assist!

[The Mad Monk]

I thought you already had your final words on the subject.

[loinburger]

He's just repeating his final word yet again, so he gets a pass

[Vanguard]

He's just repeating his final word yet again, so he gets a pass

Actually I feel I still owe loinburger a clearer explanation of why calculus can't be used to prove that this. But I can't be bothered to try to remember how to make mathematical symbols play nice with the bulletin board system.

So I will just say that you can't do it because calculus is dependent on the theory of limits.

The rest is left as a problem for the reader. Enjoy!

[loinburger]

calculus is dependent on the theory of limits.

No ****, so what?

You can't just make some asinine statement like "airplanes are dependent on the theory of gravity" and expect it to disprove airplanes

[Lorizael]

As I understand it, criticizing the lack of rigor in the theory of limits was legitimate in the 18th century, but any such flaws have long since been remedied.

[loinburger]

"GPS is dependent on the theory of a not-flat earth"

[giblets]

"GPS is dependent on the theory of a not-flat earth"

If the Earth is round, I can substitute "a round object" for "Earth". Therefore your proof for a round Earth becomes a proof that "a round object" is round which is nothing more than a tautology, rendering your proof invalidated.

[Vanguard]

As I understand it, criticizing the lack of rigor in the theory of limits was legitimate in the 18th century, but any such flaws have long since been remedied.

Wow. An intelligent comment. I can't let that pass by.

So I will jump back in for the absolutely final time to say:

I don't think there are any problems with the theory of limits....

unless you use it to try to prove that .999... = 1.