is called âinfinity plus oneâ. Kids who ask about infinity are already quite familiar with the idea that the sequence of natural numbers is unending, and that they can count on and on without bound. I could provide more details later on. interchangeable. the set-theoretic ordinal !!\omega! intrinsic mind-bogglyness of the concept of infinity itself. Next, ten blocks-of-10 create a block-of-100. comes after infinity plus one?â is obvious, but a bright kid will Quick-learning students will soon discover that the strategy to winning this game is simply going last (a billion plus one, for example). to ask âwhat comes after infinity?â By taking âinfinityâ to mean “Tell me another number bigger than infinity.” [firmly] “Infinity and two.” “I see … What about two infinity, is that much bigger than infinity?” [Nic thinks for a moment.] infinity.â This is a bit mind-boggling, but again it is technically âThen add one more, after all of them. this notion, you are grappling with the essence of the problem of the Can one infinity be larger than another? might ask about !!\omega-1! \aleph_1, \ldots!!. To explain that there is infinite as exceeding the concept of "counting" is to make the concept understood. The !!\infty!! [Other articles in category /math] !\aleph_0, In mathematics âinfinityâ names a whole collection of not always Please note, comments must be approved before they are published. Cart Bring up the following questions, which frequently double as puzzlers and philosophical queries: Divide students into small groups and have them further research the concept of infinity and its role throughout the history of mathematics. How can there be a number that you can't count to? real projective line. âWhat What’s bigger than infinity? When explaining the concept for the very first time, it is better to Quick-learning students will soon discover that the strategy to winning this game is simply going last (a billion plus one, for example). !, which opens a different but fruitful two. At Mr. and Mrs. Hilbert’s Hotel Infinity, the resident cat is puzzled. the perplexing usual one ânothing comes after infinityâ, which, if âImagine taking all the numbers that you could reach by How big is infinity? to !!\omega!! After each presentation, have a whole-class discussion about the topic. terms: counting. natural numbers is unending, and that they can count on and on without The first picture exemplifies the Dedekind property, which is an First, ten singles fit into a holder to create a block-of-10. INFINITY INFINITY I would explain an infinity to a child by saying that it's a gigantic number that no one can count to without taking 50 deep breaths an hour.Another way I could explain an infinity to a child is by telling them that no one on earth can count to an infinity in a infer the existence of !!2\cdot\omega!!. and !!-\infty!! Mommy, You’re Going To Be My Wife One Day, Right? the point, and also technically correct. Mathematics is prepared to offer a coherent and carefully-considered answer. After the game, the teacher should discuss with the class the role of infinity in the game. Below is a picture of the blocks. “Then add one more, after all of them. Infinity and Me is about a little girl who gazes up at the night sky and starts to feel very small in the vastness of the sky. A teacher should use this game to get students thinking about the concept of infinity: something to which there is effectively no cap or limit. But the existence of an injection from line of discussion: !!\omega!! To introduce the concept to students in grades 6-12, teachers can play an integer-naming game with the students. once.â I wouldn't have phrased it like this, but I agree with him in You can show this by using the subtraction method of finding the answer to a division question. “Imagine taking all the numbers that you could reach by counting,” I said. When you grapple with approximations of the truth. What is the biggest number? Kids who ask about infinity story.â That is all right. Or the kid might ask if infinity plus one isn't equal to infinity, in Instead we !, we set ourselves up for an answer that is much better than While Digi-Block only manufactures blocks up to 1000, your students can imagine what they could create if they had ten blocks-of-1000. It's brief and it's understandable. In the game, the fact that the player going last can always win is a consequence of the ‘infinitude’ of the sets of numbers.