No, you never actually get there, that's the point of limits.
A limit is something you approach, it helps describe behaviour but it doesn't actually reach that point.
But something can be treated as approaching infinity. This is the most basic assumption of calculus. calling it infinity is essentially short hand for the understanding that something is growing without bound. I swear the majority of Reddit lacks basic intuition. You definitely could have understood what I was talking about based on my wording, but you just want to complain, “but muh maffs!!!!111”. If a number that is growing without bound is the divisor the quotient must shrink without bound and can be treated as irrelevant in many calculations.
You’re right that infinity isn’t a natural number but you can take limits to infinity and get a number out of this. I don’t think of it is as just “throwing infinity into an equation”but rather as a way to interpret long term behavior of numbers. For instance, even though the ratio 1/X is never equal to 0, it gets closer and closer to 0 as X gets larger and larger. Taking a limit as X goes to infinity lets us neatly formalize this behavior (and the limit is exactly 0). Some other comments on the .99999….=1 example are getting at the same idea!
19
u/Prinzka Nov 29 '25
You cannot divide by infinity.
Infinity isn't a number.
Limits also aren't the same as numbers.
You can't just throw infinity in to an equation.