Does .999 repeating equal 1?

[loinburger]

It's fine as long as they don't inflate while still in my testicles

[Lorizael]

I just got done with related rates, so I should be able to calculate the rate at which your balloons are inflating at any given moment in time.

[kentonio]

Is it really that hard for people to understand that base 10 is not injective with real numbers?

My level of seriousness in each thread is variable, yet my need to call you an idiot regardless is constant.

[Lul Thyme]

An injective function has a unique output for each input. So f(x)=sqrt(x) is injective, because no two x-values will produce the same y value. f(x)=x^2, however, is not injective, because x=-2 and x=2 produce the same y-value. What Hauldren is saying is that the base 10 number system is more like x^2 than sqrt(x).

Note: I could be completely wrong, because I know **** all about math.

Your example is ok, but I think the first sentence should be "An injective function has a unique input for each output.".

Having a unique output for each input is the definition of a function.

[Dinner]

As was said in a previous thread: It does for really high values of nine.

[Lorizael]

Your example is ok, but I think the first sentence should be "An injective function has a unique input for each output.".

Having a unique output for each input is the definition of a function.

Hah. Oops. Yeah.

[PLATO]

Wow...I am no math person but it looks to me that this is the answer:

There is a difference between .999 repeating and 1...and that difference is exactly 0.

[Vanguard]

Wow...I am no math person but it looks to me that this is the answer:

There is a difference between .999 repeating and 1...and that difference is exactly 0.

{Socratic}But Plato, how can this be? Surely the difference between 1 and .999... is not 'exactly 0'. It is 1/infinity.

{/Socratic}

[Kuciwalker]

QED

That's actually a beautiful way of demonstrating that arbitrary properties aren't preserved under limit...

[Hauldren Collider]

My level of seriousness in each thread is variable, yet my need to call you an idiot regardless is constant.

Sorry sweetheart, this does nothing other than make you a moron, particularly when you decide to contradict me on something that is literally incontrovertible

[MikeH]

[Skyfish]

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.

[The Mad Monk]

Skyfish!?

Damn, man, where you been?

[Vanguard]

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.

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...

[Elok]

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 second line:

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

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

...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.