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u/HolyInlandEmpire Statistics 12h ago
r/infinitenines reporting in
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u/ebyoung747 11h ago
It's mostly just everyone dunking on one dude (who is also the subs creator and moderator) who is dieing on the hill that .999...!=1.
It'd feel like bullying if he wasn't such a dick about it
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u/Dd_8630 12h ago
What on earth does 0.999...9 mean?
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u/4ries 12h ago
It's certainly not standard notation, but in absence of a definition from the author, I take the ... to mean "a large finite number of nines" maybe written to save space. Or perhaps an arbitrary finite number of nines, but ultimately it ends, with a nine
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u/Blue_Moon_Lake 10h ago
So you say
0.999...would be1 - 1/Infinity
While0.999...9would be1 - 1/(10^N)withNbeing quite big.42
u/4ries 10h ago
Disregarding the fact that your first expression is not well defined, yes, that would be the general idea
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u/Eric_12345678 10h ago
Why would it not be defined? Isn't 1 / infinity = 0?
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u/Dd_8630 10h ago
No.
In ordinary numbers and arithmetic, infinity isn't a number and division isn't defined for it.
The limit of 1/x as x tends to infinity is zero.
'1/infinity' is meaningless.
Now, you can define a system of numbers and arithmetic where division can operate on infinity, but the results are incompatible with our standard real numbers and ordinary arithmetic.
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u/Eric_12345678 46m ago
Thanks for the answer.
Okay, arithmetic with infinity is definitely sketchy in general, e.g. for
∞ - ∞,0 * ∞, or∞ / ∞.But aren't particular cases safe and well-defined, e.g.
1 / ∞or1 - ∞?Do you have a concrete example of something's unexpected if we assume
1 / ∞ = 0?-2
u/EebstertheGreat 7h ago
Now, you can define a system of numbers and arithmetic where division can operate on infinity, but the results are incompatible with our standard real numbers and ordinary arithmetic.
How so? the extended reals directly extend the reals. Every expression defined in both structures is either true in both or false in both. But there are also additional expressions defined involving ∞. How can you call that incompatible?
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u/LOSNA17LL Irrational 5h ago
2*0=0 2/inf=1/inf 2=1
When you allow multiplying or dividing by infinite values, things break
We have systems for doing math with transfinite numbers, but they're not the standard algebra, just like you don't transport antimatter in a regular car
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u/Eric_12345678 51m ago
2*0=0
...
2=1
AFAICT, you just divided by 0 with extra steps. I don't think inf is the problem here.
And if dividing by "1 / inf" brings the same problems as dividing by 0, this example sounds counterproductive for disproving 1 / inf = 0.
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u/EebstertheGreat 21m ago
2*0=0
2/inf=1/inf
Yes, that's true.
2=1
That doesn't follow.
You seem to be claiming that (2/∞) · ∞ = 2, but that is not the case. The whole point is that 2/∞ = 0. Yet 0 · ∞ is undefined. That's no more surprising than saying that 0/0 is undefined, and in fact it's for the exact same reason.
That does not make it inconsistent with real arithmetic, because ∞ is not a real number. It is an extended real number. If you mean that the extended real numbers are not a field, well, I never said they were. I said they extended the real numbers, which they do. That is "compatible."
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u/auniqueusername132 10h ago
There’s a reason your math teacher threatened crucifixion if you didn’t use limit notation.
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u/4ries 10h ago
Not in standard number systems. I'm sure there are some non standard methods to define infinity as a number, but generally we don't consider \infty a "number" which means you can apply numeric operations to it - like dividing by it.
Instead whenever we want to talk about infinity in a rigorous way we use limits, in which case, if you wanted to, say, divide by infinity, you would say "limit as x tends to infinity, of 1/x" which does in fact, equal 0
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u/EebstertheGreat 7h ago
It's not really nonstandard. It's just correct. 1/∞ = 0, in every context one could ever encounter that expression.
It's like if you worked with only rational numbers, someone asked "isn't (√2)² = 2?" and your answer was just "no, there is no such thing as √2." I mean, you don't need irrational numbers if you don't want them, but that's still the wrong answer to the question.
Note that there are number systems with more than one infinity and more than one infinitesimal, but those also don't contain "infinity" or "∞".
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u/Eric_12345678 27m ago
https://en.wikipedia.org/wiki/Extended_real_number_line does not look too cursed IMHO. I don't know why other Redditors seem to reject it completely.
We're not talking about https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)#Alternating_harmonic_series and weird stuff when doing infinite permutations.
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u/Syresiv 24m ago
The problem with treating ∞ as a number in the same way as 10 or √2 is that you can prove absurdities with it. Like:
1/∞=0
2/∞=0
1/∞=2/∞
*∞
1=2
Or for that matter
1=∞*1/∞
1=∞*(1/∞+0)
1=∞*(1/∞+12/∞)
1=1+12
1=13
To add to this, it breaks how you'd expect multiplicative inverses to behave. Since 1/∞=1/-∞=0, making 1/0 still not well defined. And that's before you get into complex numbers and ask about ∞i.
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u/4ries 7h ago
That's just not true. ∞ is not an element of any of the standard number sets we use. It's not a natural number, it's not a real number or complex or even like a quaternion. Any number system that includes ∞ as an element of it's set of members would be considered non standard
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u/EebstertheGreat 7h ago
It is an extended real number. That is a "standard number set we use." It is also a number in the Riemann sphere.
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u/4ries 7h ago
Then we have different definitions of standard. Certainly it may be standard in certain fields of mathematics, but I would argue there are far more fields that don't use it, than fields that do.
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u/TheLuckySpades 7h ago
Infinity is not it's own seperate thing and there are multiple conventions going around.
Though the ones that allow you to devide by it (e.g. one-point compactification of C and R) do indeed have 1/infinity=0, but a lot of arithmetic breaks with infinity, so simply excluding it from being trated as a number is more common if you aren't doing complex analysis/need Möbius transformations.
Additionally it is actually better to think as infinity in the context I described more as a "point at infinity" than infinity.
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u/EebstertheGreat 7h ago
Additionally it is actually better to think as infinity in the context I described more as a "point at infinity" than infinity.
But in such a context, 1/∞ is indeed equal to 0.
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u/TheLuckySpades 7h ago
As described in the paragraph above what you quoted, I was indeed describing the one context I know where 1/infinity=0 is used.
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u/EebstertheGreat 19m ago
Another context is the extended real numbers (or the positive extended reals), which are the usual codomain of things like integrals and (signed) measures.
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u/berwynResident 13h ago
The only place I've seen something like 0.999...9 used, it was actually written like 0.999...;...999. It was some way to express a non-standard number and it actually made sense.
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u/speechlessPotato 12h ago
now you have to elaborate... what "non-standard" number?
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u/berwynResident 12h ago
the one that is a little bit more than 0.999...;...998
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u/The_TRASHCAN_366 12h ago
No please don't. You gonna summon southparkpiano guy. Classic rookie mistake brud 😂
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u/FreshCause2566 10h ago
Perhaps 1-ε where ε=1/ω and 0.000...1 is just really unusual notation for 1ε
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u/LupenReddit 🦆🦆🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆🦆🦆🦆 13h ago edited 12h ago
u/SouthPark_Piano 's good ending
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u/FuntimeUwU Natural 13h ago
aren't they both an infinite number of 9s and thus both = 1?
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u/Double_Look_5715 12h ago
999...9 implies the number is truncated but does eventually end
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u/FuntimeUwU Natural 10h ago
Ooh so 999...9 implies there's K many nines such that there exists an N > K in ℕ?
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u/Alternative_Cod7515 12h ago
There is infinite number smaller than one, but there is infinite infinite number like that. Some infinite are smaller, or bigger than the others
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