Current Events > What is the number between 0.999... and 1?

(+) Yeah! (+)

It's not any number that is a string of 9s because 0.999... is infinite 9s. So what is it?

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.999.... is a string of nines. Which equals 1. So there is no answer to your question. You are asking what is the number between 1 and 1. It's nonsensical.

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Ask me again a googolplex years after the universe ends.

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0.00...1

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nfearurspecimn posted...

0.00...1

That's not even a thing. Might as well say 0.00c#]@

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27
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Obviously its 42.

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Sariana21 posted...

Obviously its 42.

Ah yes

a breath of fresh air, that one is. The answer to lifes greatest mystery....!

Wait..... what was that mystery again?????

.999... is just another way to write "1"

just like 1/3 = .333...

so hard

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This is what these topics sound like in my head.

https://www.youtube.com/watch?v=RkP_OGDCLY0

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0.001

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nfearurspecimn posted...

0.00...1

This is the limit of 1/10^n as n approaches infinity. Any idea what that becomes?

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0.999... <= 1 <= 1

So, arguably, 1. Or you can get infintesimals involved, but on the real numbers the answer is either 1 or undefined, depending on how you define "between".

Here's the entire set of numbers that are between 0.999... and 1:
{ }

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Fuck infinites. I mean, they make sense and are mathmatically valid, but fuck them all the same.

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tiornys posted...

0.999... <= 1 <= 1

So, arguably, 1. Or you can get infintesimals involved, but on the real numbers the answer is either 1 or undefined, depending on how you define "between".

Infinitesimals aren't algebraic numbers and you can't use them in inequality or equality statement statements. That's like saying infinity = infinity. It doesn't make any sense.

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DuranOfForcena posted...

Absolute fools are just fools

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Tyranthraxus posted...

Infinitesimals aren't algebraic numbers and you can't use them in inequality or equality statement statements. That's like saying infinity = infinity. It doesn't make any sense.

Fair. I'm not well versed in them, just aware they exist. I assume there's some sort of parallel construction you could do with them if you wanted to?

[LFAQs-redacted-quote]

tiornys posted...

Fair. I'm not well versed in them, just aware they exist. I assume there's some sort of parallel construction you could do with them if you wanted to?

There is a number that is infinitely close to 1 but isn't 1 but the number isn't 0.999...

Infinitesimals are just the "why isn't 1/0 = infinity" answer in a way that that makes sense in the set of hyperreals.

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Tyranthraxus posted...

There is a number that is infinitely close to 1 but isn't 1 but the number isn't 0.999...

No, it is .999 repeating. That is the closest number to 1, because it IS 1.

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newhorrorguy posted...

No, it is .999 repeating. That is the closest number to 1, because it IS 1.

I specifically said "a number infinitely close to 1 but isn't 1" obviously 1, or 0.999... is the closest number to 1 while also being 1.

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Oh, we're doing this again. It's been a while.

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Tyranthraxus posted...

There is a number that is infinitely close to 1 but isn't 1 but the number isn't 0.999...

Infinitesimals are just the "why isn't 1/0 = infinity" answer in a way that that makes sense in the set of hyperreals.

Cool, thanks!

There is no number between 1 and 0.999... because 0.999... isnt actually a number itself, it's a limit. Specifically the result of 1-10^-n as n goes to infinity. And that limit is 1

You can see it here, that this number approaches 1 extremely quickly even at low values of n:

Any number on this line does not actually equal 1, but it approaches 1. And the line itself represents 0.999... going on forever


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It doesn't fucking matter

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Your mom's weight in tons.

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Purgatory+

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Gwynevere posted...

because 0.999... isnt actually a number itself, it's a limit

Incorrect. 0.999... is a constant numeric value. Numbers cannot "approach" anything they look like horizonal lines if you graph them.

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Fundamentally, "0.999..." is just a relatively confusing way of writing "1". Kind of like how 2 * 1/2 is a way of writing 1, but less straightforward.

Tyranthraxus posted...

Incorrect. 0.999... is a constant numeric value. Numbers cannot "approach" anything they look like horizonal lines if you graph them.

Numbers cant approach anything, but limits do, and that's exactly what 0.999... is.

The graph of 1-10^-n isn't actually horizontal, it's asymptotic, with its asymptote being 1.

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Gwynevere posted...

Numbers cant approach anything, but limits do, and that's exactly what 0.999... is.

Again, incorrect. 0.999... is not a limit. It is a Number. Specifically it is a real rational number. All real numbers are perfectly horizonal lines. Even irrational and transcendental numbers.

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0.9991

Whoops

You can express .999... as a limit, however. It's fundamentally just a simple infinite series that converges

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0.999... is fundamentally 1. You can evaluate the fact that it is 1 by summing the infinite series that its digits represent.

MutantJohn posted...

You can express .999... as a limit, however. It's fundamentally just a simple infinite series that converges

0.999... is a numerical constant value.

The limit as x = 1 > infinity of 9/10^x evaluates to 0.999... but 0.999... itself is a value and not a limit.

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Depending on the application & equation

.999 =\= 1

I think you're confused about divergent vs convergent series

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MutantJohn posted...

I think you're confused about divergent vs convergent series

You're confused about limits. Limits are limits. Numbers are numbers. 0.999... is a number.

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You can also have a true .999

or a true infinite string

or you can have a runoff of random numbers

Theyre very different.

.9996... or .9995... or above =\= could be rounded . Depending. But 0.9994:.. or below is really not a one, depending.

Depending on the application. You want 1 or above within a reasonable margin of error.

Actually, depending on the equation, whether you are below or above one is critical.

You can also just make shit up and assert they've always existed like an inverted double Mobius .999...

Actually, when the crow screams 3 times at midnight, even .8 is equal to 1 by the Infinicrow Superimposition.

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I edited my post

I also edited my post.

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.999 =/= 1
.99999999999 =/= 1
.999999 to a billion places =/= 1

.99999.... repeating infinitely does = 1

Hard concept for some to grasp

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You can botch your math & end up with an infinite string instead of a true 1 tho. So

.9.9

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BuckVanHammer posted...

.9.9

Now were cookin

Phantom36 posted...

.999 =/= 1
.99999999999 =/= 1
.999999 to a billion places =/= 1

.99999.... repeating infinitely does = 1

Hard concept for some to grasp

But the entire concept of limits in calculus is that a variable can approach a number without ever becoming that number. There would theoretically be an infinite amount of numbers between whatever 0.999 is and 1.

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