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

(+) Yeah! (+)

clyde_frog posted...

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.

Awesome post. Thank you

clyde_frog posted...

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.

Not quite. Because there are infinite 9's, I can prove that no matter how small a number you take away from 1, the result is strictly less than 0.999.... If it's impossible to take any amount from 1 and end up greater than or equal to 0.999..., then it must be the case that 0.999... is 1.

(those of you who have done proofs with limits, this is a pretty trivial epsilon delta proof).

1 - .001 = .999

That wasnt hard.

Xethuminra posted...

1 - .001 = .999

That wasnt hard.

.999 is not the same thing as .999... repeating.

1.0000000... (repeating infinitely) - .999999999... (repeating infinitely) = 0

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x = .999...
10x = 9.999...
10x - 1x = 9.999... - .999...
9x = 9
x = 1

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So its an infinite string of .001...

Thats the answer.

Same thing but with dots.

These are the easiest topics to troll in.

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Xethuminra posted...

So its an infinite string of .001...

Thats the answer.

Same thing but with dots.

Nope. It's an infinite string of .000000000 with no "1" at the end, just 0 forever

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That wouldnt solve the equation, mate.

Tyranthraxus posted...

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

Are you aware that 0.999... is the same thing as the sum of the series for 9/10^n?

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For a convergent infinite series, you can treat it as logically equivalent to its limit.

Ya noob.

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fifteen

clyde_frog posted...

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.

No there isn't because 0.999... is 1

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Tyranthraxus posted...

No there isn't because 0.999... is 1

In certain applications, hypothetically included, yes.

but not always

MutantJohn posted...

Are you aware that 0.999... is the same thing as the sum of the series for 9/10^n?

You are aware a sum and a limit are different things, yes?

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Xethuminra posted...

In certain applications, hypothetically included, yes.

but not always

Yes literally always.

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Tyranthraxus posted...

Yes literally always.

Got it.

Two different things are the same thing. Enjoy

Tyranthraxus posted...

You are aware a sum and a limit are different things, yes?

Why are you arguing nonsensical things that common sense can disprove?

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MutantJohn posted...

Why are you arguing nonsensical things that common sense can disprove?

No. I changed my mind. I agree. In all cases, we round up. Tell your teacher that next time you fail an equation.

What if I said that?

MutantJohn posted...

Why are you arguing nonsensical things that common sense can disprove?

You're going to have a pretty fucking hard time using anything to prove that 0.999... is not a real rational number.


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https://en.wikipedia.org/wiki/Decimal_representation

So... I dont know where you went to school but I'd ask for your money back.

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MutantJohn posted...

https://en.wikipedia.org/wiki/Decimal_representation

So... I dont know where you went to school but I'd ask for your money back.

Ctrl + F "limit" not found

Try this for further reading.

https://en.wikipedia.org/wiki/0.999...?g

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Yep

It says it right here

https://en.wikipedia.org/wiki/Limit_of_a_sequence

Read the section on real numbers.

I dont understand why this is such a debate. You seem like a smart young man but you're really confused.

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To be clear i know they're equal, pointing out there is no number between them is my favorite proof

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Whats between .999:
well that would be .001:

Youll thank me later

Hint Why round up when you can round down and whats the different to you? Something >>>> Nothing

no number is a not a solvable equation. Its no answer. Youre just rounding, dude. You can do that same thing with anything below 1.5

MutantJohn posted...

https://en.wikipedia.org/wiki/Limit_of_a_sequence

Read the section on real numbers.

I dont understand why this is such a debate. You seem like a smart young man but you're really confused.

Nah. You still don't get it. 0.999... is a constant number. It does not "approach" anything. You are linking Wikipedia articles that just state all real rational numbers can be represented as sequences which is as duh as it gets.

That's all well and good but you still don't understand that the sequence 9/10^n is not 0.999...

0.999... is what happens after you've summed the sequence 9/10^n for infinity. You're done at that point. There's nothing to graph and no limits to be taken because you've already arrived at a single static value equivalent to 1.

Graphing 9/10^n will simply show you how close you're getting to the limit after the nth iteration but 0.999... doesn't get closer to anything. It's a number. It has a value and the value does not every change. There's already infinite 9s. You can't add any more 9s to it

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Right.

Its actually not even real number. Its tangent function.

Tyranthraxus posted...

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.

lim x -> inf (9/10^x) is 0

You pull out the constant 9 and evaluate lim x -> inf (1/10^x)

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If youre looking for a number between .9 repeating and 1 there is none

daynlokki posted...

If youre looking for a number between .9 repeating and 1 there is none

You realize this is FAR from true in most REAL mathematics and its more of a brain teaser than anything.

Saying there is none is only correct if you dont round up. Thats really honestly very backwards thinking right there.

.999: + .111: = 1.11
round down and you get a 1

at least what I did involved real addition

Gwynevere posted...

lim x -> inf (9/10^x) is 0

You pull out the constant 9 and evaluate lim x -> inf (1/10^x)

sorry i dropped a word there I meant sum. And there's no need to take a limit of a summation.

Pulling out the constant 9 also doesn't do anything since the limit of 1/10^x as x goes to infinity is 0.






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Xethuminra posted...

You realize this is FAR from true in most REAL mathematics and its more of a brain teaser than anything.

Saying there is none is only correct if you dont round up. Thats really honestly very backwards thinking right there.

.999: + .111: = 1.11
round down and you get a 1

at least what I did involved real addition

Hes asking for the number between 0.999 with repeating 9s into infinity and 1. The correct answer is there is no such number. If you round, they are the same number, but nowhere did he ask you to do any rounding. He also didnt ask you to do any addition as that does nothing. If you add the same number to both, there still is no number between them.

daynlokki posted...

Hes asking for the number between 0.999 with repeating 9s into infinity and 1. The correct answer is there is no such number. If you round, they are the same number, but nowhere did he ask you to do any rounding. He also didnt ask you to do any addition as that does nothing. If you add the same number to both, there still is no number between them.

According to Bazenfruntzhillen's theorem the number can be appended to any other number to create the tiniest increment so after reaching the final 9 at the end of infinity 0.999...999 like so you add the to get 0.999.999 to create the number between 0.999... and 1.

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Whats the closest youll ever get?

.001

It is both in between and above. Thats still in between. And its more substantial than not having anything.

or, yknow what Tyrant just said. You can make another fake equation

Mathematicians love playing with infinite strings but cant handle having them as an answer

Tyranthraxus posted...

Bazenfruntzhillen's

Citation for this theorem? Doesnt even come up when copied to Google so Im gonna go out on a limb and say its bullshit.

daynlokki posted...

Citation for this theorem? Doesnt even come up when copied to Google so Im gonna go out on a limb and say its bullshit.

See post #42 in response to Xethuminra for the citation.

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So youre okay with .999: existing

but not 1.01:(thing) being only possible out?

and youre willing to literally just erase & change the answer? Get a calculator to do that. Ill be impressed.

Tyranthraxus posted...

See post #42 in response to Xethuminra for the citation.

So just trolling? Marked as such. As well as disinformation posting.

admo posted...

.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.

The answer is zero you fool.

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0 is not between 1 and 1. Did you mean to say that 1 - 0.999... = 0? Because that I would agree with.

In real life

If you create an infinite string, man, youre done. Its over.

Now, what you could do is add it and then subtract it. Which is a fun trick. But that requires having another infinite string.

a negative infinite string

a non-existent one

Or! You could subtract it and then add it, which still requires the infinite negative and a very particular one at that

tiornys posted...

0 is not between 1 and 1. Did you mean to say that 1 - 0.999... = 0? Because that I would agree with.

That's what OP is asking, "what's the difference (which is represented by a number) between a and b" AKA a - b = ?, where a = 1 and b = 0.999...

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Acceptable answers

• Nothing
• another partial number
• an equation with a subtractive infinite negating the current
• just pretend its a 1

Idk where you two went to school for math but they taught you wrong. Definitely ask for refunds lol.

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