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I thought that most of us learn at an early age, as a result of this kind of exchange, that "infinity" is not "the biggest number" or even a number at all, as f
by bhk 3y ago
I thought that most of us learn at an early age, as a result of this kind of exchange, that "infinity" is not "the biggest number" or even a number at all, as far as the ordinary notion of "number" goes.
- JKCalhoun 3y agoMy child mind conflated infinity and God. Or maybe I was correct, I have no idea now.
- ASalazarMX 3y agoThat was the adults attributing infinite and contradictory powers to their god. Church sermons will frequently mention infinity.
- selcuka 3y agoHistorically, anything that can't be easily comprehended has been attributed to a higher power.
- thedailymail 3y agoYou're not alone! Georg Cantor was deeply concerned about the theological implications of his work on transfinite numbers, to the point that he wrote letters to Pope Leo XIII to explain why the new infinities were consistent with a God of an even higher order of infinity.
- NegativeK 3y agoNo math instruction I had ever discussed infinity with any rigor until calculus -- and even then, it was only infinity as a limit. Infinity as a concept was brushed off in the same way that the square root of negative one was brushed off until we were actually taught about it.
- NegativeLatency 3y agoIt came up a bit in some physics classes, when you can mathematically make something go to positive or negative infinity being able to remove it from the simplified calculation of something is very handy.
- tesseract 3y agoOn the one hand I get why that is - the calculus notion of infinity is the one that tends to be useful in applied math - on the other hand it's a shame because the set theoretic notion of infinity has more to offer to someone trying to ponder the nature of the infinite. Or put another way, "what's ∞ + 1" basically invites the non-answer "that's not a well-formed question" whereas "what's ω + 1" gives you a whole intellectual thread to pull on.
- NegativeK 3y agoI've always been disappointed that number theory, set theory, etc aren't introduced in middle school or high school. It makes sense, since those are a lot less useful than the subjects that are taught, but something like number theory is incredibly approachable to a middle school student. And it can show students that math can be a lot less about memorization and a lot more about creative thinking w.r.t. proofs.
- bhk 3y agoI would argue that "that's not a well-formed question" is a correct answer, not a non-answer. ...and that the intellectual thread you are pulling on is a (more) artificial notion, constructed by set theorists for the sake of set theorists, not for the sake of counting or measuring in any real sense.
- NineStarPoint 3y agoI’d disagree personally. The idea that you can add things to an infinite set, or multiply an infinite set are actually useful concepts. If you imagine the universe is infinite and as such has infinite stars in it (ω) you could discuss how some infinite universes have twice as much star density as our infinite universe (ω2). Or imagine taking a copy of our universe and adding a single star 10 light years from earth (ω+1). In a very real sense the second universe would have twice as much stuff in it as the first universe, even if you can countably map the two universes to each other. Or maybe put another way, taking the idea that infinity is just infinity makes a lot of sense when you’re primarily considering non-infinite numbers. When you’re primarily considering the concept of infinity and what you can do with it mathematically though, using systems that let you describe infinity with more nuance makes a lot of sense.