I don't know where so many people got this misconception from, but 0.999... does not equal 1...

I don't know where so many people got this misconception from, but 0.999... does not equal 1. Numbers have a unique decimal representation and by writing 0.999... you explicitly denote a number which is infinitesimally smaller than 1.

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This. Math is completely retarded. Like for example adding 1+2+3+4 and so on gives you -1/12. Wtf? It is obviously infinity. If you disagree you are a fucking retard, same with the 0.999... Math is stupid.

nice bait thread retard

I always just assumed it was basically just because our mind can't even comprehend such a small difference. It makes sense to use the repeating decimal for formulae and such but when I think of a number I think of items. So if someone says 0.999.... I think of like an apple that brushed up against something rough
To add, I've only seen redditfags say they're the same thing, just to bd quirky I guess

Stupid math magicians. Like, I can see the two things are different, stop making shit up like rounding.

>Numbers have a unique decimal representation
Prove it

this. give a proof faggot your words are meaningless.

>Numbers have a unique decimal representation

Okay, so 0.999... , 0.9999... and 0.99999... must be different numbers then

Real numbers have two representations. For 1, the other one is 0.999... Just because it looks different, it doesn't mean it's literally different. Otherwise you can tell what the difference between the two is, right?

1/3 = 0.333...
3 times 1/3 = 3 times 0.333... =1
3 times 0.333... = 0.999... = 1
0.999... =1
Retard

Are you able to name some practical examples of where taking 0.9999999999999999999999999999999999999999999999999999999999999999999 as 1 would be detrimental?

I didn't think so, you little shit

math is a scam

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A recurring decimal isn't real. It's an abstract concept, like infinity.

They aren't aren't same thing, no. However they are PRACTICALLY the same thing as in practicality a difference that miniscule seldom causes any sort of errors.

Okay, let's play with this a lil. Suppose that 0.999... isn't equal to 1, but instead a unique (irrational) number whose difference from 1 is infinitesimally small. First we can conclude that there is no number between 0.999..... and 1, as the difference between this new number and 1 cannot be smaller than the difference 0.999... and 1, as it's already infinitesimally small (otherwise it would suggest that there exists a number smaller than an infinitesimally small number). Now, take the open interval (0, 1) on R (so it's an open set on the standard topology). However, this cannot be an open set, for it's equivalent to the set (0, 0.999...], which contains one of it's limit points. Furthermore, you can suggest it contains it's lower limit as well, by defining it as (1-0.999...), so the open set (0, 1) is actually the closed set [1-0.9999..., 0.99999...].
Inherently this doesn't "prove" that 1 = 0.999... (doing so is trivially easy) but it goes to show that if you assume it to be false, you'll get some wacky results.

you assume 1/3 = 0.333...
circular logic

Nice circular reasoning faggot, but
>we can conclude that there is no number between 0.999... and 1
(0.999... + 1)/2
Here, I found a number between them.

Not exactly. What would the difference be between (0.999...+1)/2 and 1 be? And how would that compare to the difference between 0.999.... and 1? In fact, care to write out what the decimal representation of (0.999...+1)/2 would be?

1 - 0.999... = 0.000...1
(1 + 0.999...)/2 = 0.999...5

>Numbers have a unique decimal representation

Dont tell this faggot about pi or any irrational numbers for that matter

Care to show me two different decimal representations of pi?

So you're willing to suggest that between 1 and 0.999... there's a 0.999...5? There's a few issues with that. Since 0.999...5 contains an infinite series of 9s, you'll never be able to place the 5 anywhere exactly. And again, what's the difference between 0.999...5 and 1, compared to 0.999.... and 1? The latter is defined to be infinitesimally small, are you suggesting there's a number smaller than an infinitesimally small one?

length of exposure to your mom

>Since 0.999...5 contains an infinite series of 9s, you'll never be able to place the 5 anywhere exactly.
N (the natural numbers) is an infinite ordered set. Yet you can define the union of N and {-1} and still have an infinite ordered set. Your argument is debunked.

>And again, what's the difference between 0.999...5 and 1, compared to 0.999.... and 1?
0.000...5 obviously

>The latter is defined to be infinitesimally small, are you suggesting there's a number smaller than an infinitesimally small one?
If x is an infinitesimal number then obviously x/2 is smaller than x.

my point is that pi and irrational numbers can't be represented as a decimal because it they are infinite

I like to get stoned and do maths, inbetween doing maths, I masturbate like a fucking demon

They can though. You can compute the n-th digit of pi for any n.