Well?

0.999... is always 0.000...1 close to 1, so no

>claiming a mathematical fact without showing a mathematical proof

I can tell OP is uneducated and doesn't do any sort of computational work. Go try it on a computer and see what happens.

1-(0.9...) = 1/inf

Quads of truth

1 - 0.9 = 0.1
1 - 0.99 = 0.01
1 - 0.999 = 0.001

Therefore, 1 - 0.999... = 0.000...1

1/3 = 0,333...
3 * 1/3 = 3 * 0,333...
1 = 0,999...
qed

this isn't a proof.
why does the final equation hold? all you have shown is simple subtraction. why do the first three equations imply the final one?

1/3 =! (0.3...)

It is out by the same margin of error as (0.9...) =! 1

1/3 has a functional limit of (0.3...) but it only ever approaches it

1/3 cannot be accurately represented as a decimal in base10.

>isn't a proof.
It is actually

>0.9999... * 10 = 9.9999... || -0.9999...
>0.9999... * 9 = 9 || /9
>0.9999... = 1

X=0.9... /*10
10X=9.999...
-
9X=9 /9
X=1

No. It's always less than one, however infinitesimally small. It will never be one, and therefore cannot be one.

Two numers are identical when there is no third number between them.
So yes, 0.9999... = 1

Easy proof.
0.999999... x 10 = 9.9999999...
9.99999... - 0.999999 = 9
So 10 x 0.99999999... - 1 x 0.999999999... = 9
9 x 0.99999999... = 9
0.999999... = 1

To imply that repeating digits of 9 at the end will always have a 1 at the last decimal place of its difference when subtracted from one

>infinitesimally small
Correct

However math tends to simplify this for mainstream consumption so they don't have to process irrationals and deal with infinity

There is a number between them

1/inf

Wrong

Thought only /sci/fags were discussing this shit.

Nope. There is no number as 0.(0)1.
It would be right if the infinity was a finite number, which is by definition is not.
Read a book.

No it isn't. Those are two different versions of the same number, much like 1/2 and 0.5 are the exact same number.

>they are seperated by the reciprocal of infinity
...which literally does not exist, meaning there is no separation at all

except it's wrong

So are you saying infinite decimal places don't exist? So 0.999... doesn't exist?

It would have been for a finite number of 9s, but they're infinite, so elementary grade math does not work.

...which equals exactly 0.

The reciprocal of infinity absolutely exists. The concept of infinity is relied upon to achieve (0.9...) in the first place. How many 9's do we queue up after the decimal if infinity does not exist?

Infinity exists.

As does it's reciprocal, the infinitesimal.

Which is the gap between:
1 and 0.9...
1/3 and 0.3...

depends on your measurement uncertainty. Within maths this doesn't hold up, as it's a made up syntax with ideal situations. In engineering this will almost always hold up because we're not compulsively obsessed about numbers like those doctorate nerds

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In grade school math sure

No, that doesn’t even make sense.
>1/2 = 0.5
>1/3 = 0.333...
>1/4 = 0.25

If the denominator gets bigger the closer it gets to 0. Not 1. So the reciprocal of infinity is close to 0 not 1. (Can also be argued graphically)

no. the acceptable equivalency is only because at certain levels of precision, computers fail.

i had a project in parallel programming where it was a bunch of circles of random size (within reason), randomly placed in a field, that would then have "gravity" applied to them based on size. that would cause them to attract towards each other and bounce off of each other.

the problem is that no computer can properly calculate floating point numbers, so there had to be a buffer because if they were not controlled that way, they'd intersect potentially and then end up being shot away from other at light speed rather than bouncing.

a computer will say that 0.9999999999999 is 1 because it fails and rounds. i have a cute calculator app on my android phone called "simple calculator" that demonstrates the failure of floating point in the ARM cpu. the same happens in any CPU.

essentially, since because our greatest calculators can't do any better, 0.999999999999 is 1, but it really IS NOT. if you understood math, you'd know that there is the concept of "countably infinite" (integers) and "uncountably infinite" (floating point numbers). it's actually easy to prove that there is no way in the universe to count all the numbers from 0.00000000000000000000000000000000000000000000X.

youtube.com/watch?v=zdYjdCh3WUo

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Wow it amazes me how dumb americans are

>1/3 = 0.333...
Fail

how???

ThE rEcIpRoCaL oF iNfInItY

>this
it all depends on what measure of uncertainty you choose to accept. If you accept 1 decimals of uncertainty you'll round up to 0.999 => 1.00

If you accept no uncertainty you'll find that 1.0 =! 0.99999. Can be graphically represented with differential mathematics

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The problem with everyone who thinks 0.999... =/= 1 is that you seem to think 0.999... isn't a number, insisting that there's some number 0.000...1 at the end separating it from exactly 1. There isn't. 0.999... to infinity exists, and it's not a process, but an exact number, that's exactly 1.

There's nothing wrong with intuition, but as is true in higher mathematics, philosophy and often sciences in general, intuition isn't everything. This is why the tools of mathematics, philosophy etc. exist - to help us overcome our intuition that often tries to mislead us.

Falling back on this intuition and insisting that it's correct over the carefully constructed and proved tools is a kind of romanticizing bullshit that's the reason science can't get enough funding. There's a really good reason why it takes 6 years in a university to be a mathematician.

(0.3...) only approaches 1/3. It never completes the journey

Same with (0.9...) and 1

You guys do realise that this isn't actually up to debate? There's a wikipedia article on it, en.wikipedia.org/wiki/0.999...

Go read it.

Mate differential math and limits sets the picture for this in advanced high school maths.

Perhaps if you had taken it instead of woodworking you would understand

In decimal 0.99 recurring will always be less than 1. More basically put, when you buy something that costs 0.99 and you pay with a 1 dollar / pound whatever, does the cashier give you 0.01 change or say "ah that's the same as 0.99 so no change"?

I actually took theoretical physics, but okay then.

If you understand the concepts of limits and differential mathematics, I honestly can't fathom how you'd advocate for 0.999...=/=1

that's kind of funny. it's either an example of when ultimately left brain math fuckheads try to be right brain trippy or a joke on purpose.

one number does not equal another. i think we can start and end there.

i got dubs so i can gloat but also to add:

i am getting a B in my last CS course and just for my own balls, i took calculus 1 FIVE FUCKING TIMES and discrete math twice to get a good grade and know it.

limits can suck my ass. read that stupid wikipedia article. it suggests that it's just a "method". ok, well limits are a method to figure out that something approaches.

pause the simulation, einstein, and observe that it's still not actually 1.

All these 'experts'.
Technically 0.999...has no value. True numbers are written as angles to represent their value and the 9's in this thread have no motherfuckjng angles therefore no value.

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0.99 and 0.99... aren't the same number? The fuck are you on about, get out of here.

best answer yet

Kek

1/3 is an equation.
.3333~ is a decimal equivalent
Let's move this to application.
Use engineering and say this pin needs to be 1/3".
My previous knowledge says this high-precision widget should work with a .0003" tolerance window.
Pin can be .33315" to 33345".
Exact numbers like that don't exist.
They don't matter.
3/9 = 3 etc.

No that's complete bullshit.

the '...' is practically 1, but never going to be 1.