Does .999 repeating equal 1?

[Vanguard]

...which, according to the conclusion, equals nine. I'm not 100% certain here, but you might actually be criticizing this proof for *not* begging the question.

The proof depends on it being equal to 9. We cannot postulate the thing we want to prove.

[loinburger]

The sum of an infinite geometric series is a/(1-r) where a is the initial term and r is the ratio between successive terms; .9-repeating is the geometric series with .9 as the initial term and .1 as the ratio between successive terms, which results in the sum .9/(1-.1) = .9/.9 = 1

[KrazyHorse]

The proof depends on it being equal to 9. We cannot postulate the thing we want to prove.

Are you an idiot?

[Vanguard]

No. Are you?

[Elok]

If we have proven that the two are just different ways of writing the same thing (and the reasoning is pretty airtight AFAICT), then whether it is presented as one or the other is irrelevant.

[Lorizael]

Yeah, but it's a lot harder to write out an infinite number of 9s.

[KrazyHorse]

No. Are you?

I disagree with your claim.

[giblets]

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...

So you've proven that if .999... equals 1, then 9 is equal to 8.999...

[Hauldren Collider]

NO WAY

[DaShi]

The real question is: does .888 repeating equal .999 repeating?

[giblets]

Maybe it will with a sufficiently large number of 8's.

[Vanguard]

So you've proven that if .999... equals 1, then 9 is equal to 8.999...

No. I haven't proven that. And neither has Starfish.

[giblets]

No. I haven't proven that. And neither has Starfish.

It's not self-contradictory. How does replacing 9 with 8.999... contradict 1 = .999... ? You're not making any sense.

[Vanguard]

Wow. The Silly Proof is usually good for a lot more yucks than this.

This place just doesn't get the traffic any more, does it?

[Asher]

Asher thought that .9 repeating isn't one?

Asher, are you sure you're a compsci major?

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...