![]() So you run into two problems, the problem of it not being immediately obvious (common sense), and the problem of conceptualizing infinity. Then you hit the infinite jump, and suddenly it becomes true. 999999999999(a ridiculous but non-infinite number of times)? Most grade school kids would say "no", and be correct. Why? Because your mapping two concepts that we all were taught as a kid isn't true. When presented with it, my first reaction would be "Hell no! Stupid.", even though I know it is true. Let me qualify that a bit, I intellectually and academically know it, but on a softer, more psychological level, I don't actually believe it. does not equal 1/3, and for many of the same reasons.įor once in my life I can claim someone is underestimating the average person! does not equal one also believe that 0.333. would not quite be the same as 1, as the former is a real and the latter is an integer, so despite having the same value their different types would mean they could not be used identically in all circumstances. Of course, in an insanely strictly typed language with infinite precision 0.999. = 1" introduction to the remarkably dull fact that you can represent the same value in different ways. My guess is that they are simply not very smart, as anyone who isn't fairly dumb would see that there is an obvious pedagogical problem at play here, and correct their presentation accordingly, rather than blindly and stupidly repeating the rote "0.9999. I'm not sure why people insist on presenting this result in the most counter-intuitive way possible and then wasting vast amounts of time trying to undo the damage they've inflicted with their incompetent introduction of the problem. You can of course also represent 1 as 5*1/5 1/2+1/2 and all kinds of other awkward and unintersting ways, too." ![]() It's just a different representation of exactly the same value. Now curiously that also means you can represent 1/1 = (3*1/3) as 3*0.3333. You know you can represent 1/3 as 0.3333. We all know this, and it's completely uninteresting, but I'm going to bore you with it anyway. If instead they said, "It is possible to represent numbers in different ways. They set it up deliberately to create a block in other people's minds that makes it unnecessarily difficult for them to understand what is being claimed and why it is true. Nope, the problem is that the people who discuss this question are lousy teachers. The problem with that, though, is that people have trouble accepting that there was nothing wrong with what they did - a lot of people have this implicit assumption that if a few simple steps bring them to a result that doesn't look like it makes sense, then they did something wrong.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |