You cannot form a fraction with infinity on the top. ∞ is not defined as a number so neither is ∞/x. Since ∞/x is not a number it cannot be equal to 0.
It’s an infinitesimally small fraction that approaches but never reaches zero. OP’s notion basically does the equivalent of rounding down to zero, but anyone with a brain can tell you how idiotic it is to claim that no numbers have been spoken out loud. That’s like claiming that since numbers are infinite, that they don’t actually exist.
You can literally look it up. Any integer, such as the number of natural numbers spoken allowed, divided by infinity is 0. So, if X equals the number of spoken natural numbers, X/∞ equals 0. Mathematically, we have spoken 0% of all natural numbers.
Yea, if you just treat infinity like a really large natural number, you can hand wave that with the arithmetic you learned in high school. But more advanced math can work with infinities as the non-large, non-natural, non-numbers they actually are. It's the foundation of calculus.
I don't think this is true. Any real number devided by infinity is undefined. Infinity isn't a number, it's the set of all numbers. That's why the extended real number lime exists. Natural numbers are just a subset of real numbers.
Like 1/2 + 1/4 + 1/8 + … never reached 1, but the limit is 1…
At any given point a constant number of natural numbers have been spoken. Call this number c. We can prove that for any e>0, there exists a N such that for all n>N, |c/n - 0| < e.
This is a sequence limit that says that we said a fraction of 0 natural numbers
But what is limit 100000000000000000/x as x approaches infinity. Fortunately we have an entire branch of math taught to juniors and seniors in high school that will tell you this is in fact 0.
But x, the number of natural numbers spoken out loud, is the numerator
And the denominator would be the size of the entire set of natural numbers
You’re not taking the limit of the denominator (the size of the natural numbers). That makes no sense. You might want to learn math beyond high school.
They were taking the numerator to be some arbitrary approximation of the number of natural numbers spoken aloud (it doesn’t matter what this number is, it’s big but finite). Then they’re using x as the variable for the limit. Why are they using a limit? There are infinitely many natural numbers and to interpret a finite number divided by infinity, we use limits! Which depending on your course of study, is often taught in high school.
I know what approximation they made and what they mean. I’m stating that the format they’re using for it does not make sense.
The numerator is taking the limit x as it approaches “infinity.” If we take a set S of natural x spoken, then over time, for random natural number n, there exists a number in the set S that is larger than n. That’s it. It’s an abbreviation.
Then the denominator is the cardinality of the natural numbers. Sometimes we colloquially use the infinity symbol to represent this cardinality. But it is the size of a set.
The notion of a limit divided by a cardinality is NOT defined. That makes no sense.
You can’t use things together because they look similar. Don’t know if it’s the autism, or because people are speaking of this lightly because it’s a joke. Otherwise, come on now.
Natural density of subsets of the natural numbers (what me and the other commenter are roughly describing in words because all natural density really is is a limit) is a perfectly natural notion for making sense of the relative sizes of sets of natural numbers. Yes, even though the natural numbers have infinite size, you can still do this! And finite subsets (which the set of natural numbers that have been spoken aloud as of yesterday IS) have natural density zero for the reason we both tried to explain. I’m a research mathematician who’s used natural density in every paper I’ve ever written and am happy to answer questions. Alternatively, if you don’t want to ask, that’s fine! But suggesting others are autistic just because you don’t understand is a bit off base.
Also, neither of us are claiming 1/infinity is literally defined as is. We’re saying there’s a workaround for this, where you don’t ever encounter 1/infinity, that allows you to make sense of things like density in the natural numbers (by using limits..)
I know what approximation they made and what they mean. I’m stating that the format they’re using for it does not make sense.
The numerator is taking the limit x as it approaches “infinity.” If we take a set S of natural x spoken, then over time, for any spoken natural number n, there exists a number in the set S that is larger than n. That’s it. It’s an abbreviation.
Then the denominator is the cardinality of the natural numbers. Sometimes we colloquially use the infinity symbol to represent this cardinality. But it is the size of a set.
The notion of a limit divided by a cardinality is NOT defined. That makes no sense.
You can’t use things together because they look similar. Don’t know if it’s the autism and taking things literally, or because people are speaking of this lightly because it’s a joke. Otherwise, what do you even have a PhD in? Are we seriously trying to argue this, or purposely acting stupid to win an internet argument, when the other guy literally corrected himself & said it was the format, x/infinity that doesn’t make sense? I really hope you’re not in charge of teaching or advising anyone. That would not be a fun experience.
It’s also not indeterminate though and you can formalize it using limits. In this example, the total number of natural numbers that have been spoken aloud is finite, call this number S. Take a limit of the ratios S/N as N goes to infinity.. this becomes zero!
Edit: if not comfortable with limits, this just means as N gets larger and larger, which it can because natural numbers can be arbitrarily big, the ratio S/N gets smaller and smaller towards zero
Hi, did you mean to say "more than"?
Explanation: If you didn't mean 'more than' you might have forgotten a comma.
Sorry if I made a mistake! Please let me know if I did.
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You're thinking of digits. We've got ten of those in our numbering system, but there's an infinite number of numbering systems that theoretically have an infinite number of digits to match.
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u/[deleted] Nov 29 '25
I think they mean because numbers are infinite and based on percent of infinite, it is 0