Does 1 = 0.9999999999…?
This being the internet and all, it might not surprise you to find out that the question of whether 1 = 0.9999999… (infinitely repeating 9’s) is a pretty hot area of argument across message boards and blogs, because people will argue about anything on the internet.
But this argument has actually been raging for some time. I was listening to an interview with math dude Steven Strogatz on NPR’s Science Friday when I was reminded of it. Strogatz has a cool-sounding new book out called The Joy of X, that explores how math, when you disconnect it from all those ugly chalkboard proofs, is fascinatingly intertwined in every part of our lives. So why the controversy? This problem messes with our idea of what “equals” means. It just gets a little wacky when we apply logic that is meant for words to the world of numbers. There’s even a Wikipedia page dedicated to the number.
In the real number system, 1 can be shown to equal “0.999…” pretty easily, although that doesn’t necessarily explain why it is the way it is. That’s a discussion for you and your math professor.
Here’s your thought experiment: Take a pie. It represents “1”, a whole pie. Cut it into 3 equal pieces, each representing 1/3, or “0.333…” repeating. Put those pieces back together and you have a whole pie, or 1 (assuming you didn’t lose any crumbs). Get it? Pretty weird.