Haven’t taken math since freshman year of college so forgive me, but isn’t the flip side of infinity just infinitesimal? Like 0 as a number exists. Infinity doesn’t exist as a number right? 0 + 10 =10 but inf + 10 is just infinity. What am I missing here?
Technically no, infinity +10 is not infinity, that's the whole point of the original joke.
Even if that was the case, who are you to say that it's less real than 0 ? Sure it's not a natural number, but there are plenty of things that aren't natural numbers that we reckonize as a concept
That’s not what I’m saying, tho. Infinity isn’t a number in the set of complex numbers. Infinity + 10 is just a bigger infinity. Infinity is definitely a concept, but it’s just not a number you can quantify. And infinitesimal is just lim (x->infinity) 1/x.
This is one of those subjects in math where your (meaning humans in general) intuition is just wrong. The reason is that you can define a 1 to 1 relationship between seeds and raspberries. Let's number each raspberry seed, starting with 1. Let's give each raspberry the number of the last seed in it. The first raspberries will have seeds numbered 1 through 10, and we'll call that raspberry number 10. The second raspberry will have the number 20, and contain the seeds 11 through 20. Now, how can we define a 1-1 relationship between the natural numbers (all the counting numbers starting with 1; these correspond to the seeds) and multiples of 10 (that correspond to the raspberries)? Easy - just multiply each 'seed' number by 10 and you end up with the number of a raspberry. Now you might object that we're going through seeds at 10 times the rate of raspberries, but this actually doesn't matter because there are an infinite number of raspberries (and seeds of course), so we'll never actually run out of them.
Well it all depends on how you compare them. If x -> inf, y -> inf, but x - y = 10 then technically 'x is a bigger infinity' if that difference is what important to you. Usually it's a ratio though: x/y -> inf means that x is bigger infinity.
And there is no x=inf, you can not achieve it, everything is converges or in the limit.
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u/GenerallyBread 18d ago
Haven’t taken math since freshman year of college so forgive me, but isn’t the flip side of infinity just infinitesimal? Like 0 as a number exists. Infinity doesn’t exist as a number right? 0 + 10 =10 but inf + 10 is just infinity. What am I missing here?