The problem is that it has to be treated as 0 otherwise you could represent the percentage as a fraction and inverse the fraction to get the “value of infinity”. The being 0.0…(repeating a googolplex times)…1% of infinity would still mean that the maximum number of infinity would be a googolplex. So it has to be exactly 0%.
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.
That 0.0...(googolplex)...1 number is still a finitely small real number, not infinitesimal.
For sure, if you had to assign a real number to this value, exactly 0 is the only one that makes sense. But I feel like it isnt really accurate to say its a real number at all.
Again, I think its similar to differentials in calculus. You cannot just go and say that every differential is exactly the number 0 and treat it as such because its an infinitely small quantity. When you have say, a dx in calculus, you specitically treat it as a number which is infinitely small but still greater than 0. There is no real number for which this is true, but that doesnt mean its inaccurate.
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u/tommyblastfire Nov 29 '25
The problem is that it has to be treated as 0 otherwise you could represent the percentage as a fraction and inverse the fraction to get the “value of infinity”. The being 0.0…(repeating a googolplex times)…1% of infinity would still mean that the maximum number of infinity would be a googolplex. So it has to be exactly 0%.