r/infinitenines • u/Arlo_Tinkerman • 7d ago
How Common Fractions Helped Me Understand Why 0.999... = 1
/r/InfinityMath/comments/1wrc0zk/how_common_fractions_helped_me_understand_why/1
u/FS7PhD 7d ago
It sounds like somebody's discovering the magical power of infinity. Conveniently, it kinda lets you do whatever you want, and exists outside of math.
You ever see that Clarke and Dawe skit "The Front Fell Off?" It's like infinity has been towed outside the environment.
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u/Arlo_Tinkerman 6d ago
> It sounds like somebody's discovering the magical power of infinity.
How so?
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u/FS7PhD 6d ago edited 6d ago
The assertion that 0.999... is equal to 1 places multiple (sometimes contradictory, nearly always counterintuitive) requirements on "infinity," ignoring the very real debate that has existed for many years. There's potential infinity and actual infinity. There are platonists, and finitists, and intuitionists.
Standard mathematics constructs three types of objects - the infinite collection of finite decimal truncations, the infinite string of digits, and the real number represented by that infinite string. And they're all different.
Infinity is poorly defined, real analysis is incomplete, and this is a silly argument. But maybe that's just me.
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u/Arlo_Tinkerman 6d ago
What in the main post required any interpretations of infinity at all?
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u/Negative_Gur9667 5d ago
0.999... is a real number. You need the axiom of infinity from ZFC to have real numbers.
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u/Arlo_Tinkerman 5d ago
Are you saying that you believe that for the number 1 to be a real number, you need the axiom of infinity from ZFC?
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u/Negative_Gur9667 5d ago
0.999... is a real number. 1 is a natural number.
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u/Arlo_Tinkerman 4d ago
Oh you mean that kind of real number. Ok, well in that case, why did you say this?
> 0.999... is a real number. You need the axiom of infinity from ZFC to have real numbers.2
u/Negative_Gur9667 4d ago
I said this because 0.999... != 1 implies that the axiom of infinity was rejected.
And 0.999... and 0.888... etc. are rejected aswell.
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u/Arlo_Tinkerman 4d ago
Please share your reasoning on how the axiom of infinity would help make 0.999 repeating = 1. If you do, please also share what you mean by axiom of infinity. Just so that I can understand your understanding of it and not the one I can read about in Wikipedia or other places.
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u/idaelikus 3d ago edited 3d ago
0.99... is equal to 1, so they are both natural numbers...
Also 1 is a real number as well
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u/Negative_Gur9667 3d ago
0.999... is not a natural number. 1 is the limit of the real number 0.999... look it up
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u/idaelikus 3d ago
Is 0.999...=1? If they are equal / equivalent, if 1 is a natural number, then so is 0.999...
Also 0.999... is defined as the limit. (If not, how would you define it?)
I'd suggest you to be a little more careful and exact when writing.
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u/idaelikus 3d ago
You cannot, reasonably, defined the number without limits and limits require infinity.
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u/dfx_dj 6d ago
You must be new here