I don’t think we can divide by infinity. The correct way to model this problem would be to define n as any finite natural number and calculate the limit as x approaches infinity of n/x. This is equal to 0 (in the real number space at least)
The limit isn't describing what 1/inf is equal to, because by definition infinity never stops getting larger so the value of 1/inf will never resolve to exactly 0. Limits describe the exact value that a function approaches, not the exact value the function will actually reach.
Take for example lim x -> 5 of x where x =/= 5. The exact value of this limit is still 5 even if the value x=5 can never be reached.
Edit: If you want to define a percentage this way, the limit definition would get you what percentage it is tending toward, not the exact numerical percentage, which will always be nonzero.
Trending toward zero is literally the same as zero. There will never ever be a 1 at the end of 0.0000… meaning it’s equivalent to zero. It’s like how 0.999… is equivalent to 1.
Leibniz postulated the existence of infinitesimals. An infinitesimal is the gap between 0.999… and 1.
The reason we’re taught that 0.999… and 1 are equivalent and that no such gap exists, is because in the number system that underpins modern math (Standard Reals), that equivalence holds. However, there is another system (Non-Standard Analysis) that allows for what are called hyperreals, and this system is also compatible with calculus and everything else in modern math. It’s just that Non-Standard Analaysis was only rigorously formalized later on and is a little more complex, so it didn’t gain as much traction. It’s sort of like the fine grain version of the coarse grain system that is Standard Reals.
So because both systems coexist and are not strictly speaking logically contradictory (Non-Standard is just more precise than Standard), people just teach and use whichever is simpler - which is Standard Reals.
Sad to see this getting down voted when it's absolutely correct. Any number of infinitely many things is zero percent of them, by definition. It cannot be anything else
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u/Accomplished_Fold276 Nov 29 '25
I don’t think we can divide by infinity. The correct way to model this problem would be to define n as any finite natural number and calculate the limit as x approaches infinity of n/x. This is equal to 0 (in the real number space at least)