Can we find a one-to-one mapping from (0, 1) to [0,1]?

Sure. Find some infinite sequence [math]a[/math] of distinct values in [math](0,1)[/math]. You might use [math]\frac12[/math], [math]\frac13[/math], [math]\frac14[/math], [math]\dots[/math]. Th…

Top stories for Long   Can we find a one-to-one mapping from (0, 1) to [0,1]? Phil Scovis, I play guitar. And sing in the car. • Answered August 11 Sure. Find some infinite sequence [math]a[/math] of distinct values in [math](0,1)[/math]. You might use [math]\frac12[/math], [math]\frac13[/math], [math]\frac14[/math], [math]\dots[/math]. That's just a suggestion. There are many to choose from. It ... Read more » 46 15   There is an anecdote that tells of the time Bertrand Russell was explaining to his students that an argument that starts from false premises can have any conclusion. Alessandro13 • Posted Nov 27, 2024 One of his students stood up and said to him, "Starting from 0=1, prove to me that you are the pope." Russell replied, "If 0=1, then, adding 1 to both sides, we have that 1=2. I am one person, and t... Read more » 973 82   What's the backstory on famous food labels? Britney Vu, A curious Educational Anthropologist • Updated January 31, 2020 We all know, have seen or eaten raisins from Sun-Maid, right? Now the question is, how did the iconic girl with a red bonnet get on the packaging's logo in the first place? W... Read more » 2K 38   Is the existence of polywater the greatest scientific discovery of the last century? T. Barczuk, studied at Gdansk University of Technology • Answered August 9 Polywater caused a furore in the scientific community in the 1960s when Soviet scientists announced the discovery of a new polymerized form of water. It was the time of the... Read more » 1.4K 54   Isn't it almost impossible to bankrupt a casino? Ty Doyle, A lawyer with an opinion on everything • Answered July 14 Not at all. A casino has generally been viewed as a license to print money, so losing money on casino operations would be very difficult to do. But everything else that is ... Read more » 279 42   What is a brain teaser that is very short and extremely hard for adults? James Carter, Student (2017-present) • Updated April 17, 2018 This is the perfect brain teaser that has a rather tricky solution. There are two people in front of a door. Behind each door is either happiness or misery. The people in fr... Read more » 313 33   Why don't we use the fastest possible processors in all devices? Dapid Candra, Supporting users 👥 😊 🔥 • Updated March 23 Let's see. The fastest available processor is now (March 2025) AMD Ryzen Threadripper PRO 7995WX. The 7995WX is a massive workstation CPU that requires a large motherboard (... Read more » 911 71   Historical Pictures That Will Give You Chills Shubhr Gunjan, studied at DAV Public Schools, India (2023) • Updated May 19 1. Soviet soldiers guard a liberated "holocaust train", the passengers unfortunately did not live long enough for their liberation. - 2. A Frozen German soldier used as a checkpoint "sign" - 3. Soviet ... Read more » 3.9K 161   Are newborns really that difficult to care for? Melanie Lord, Registered Nurse (2009-present) • Answered March 14, 2019 No actually. And yes. As a fourth time mom and someone who works with newborns all the time, no. As a first time mom - well, I still didn't mind it. But, it depends on the ... Read more » 581 51   What great song was "ruined" once you really listened to the lyrics? Tom Stalnaker, Nearly 50 Years Work for State Government. at WV Tax Dept/Contracts with Counti... • Answered June 27 Not me but a lady on the radio call as I was digging a sewer line for my father and she asked the DJ to play that religious song. He ask which one. The lady said the one th... Read more » 897 119   How can we construct a function such that f(f(x)) =-x? Obviously, this function cannot be continuous on R, but can we construction a discontinuous function on R? Furthermore, does it exist on C? Alon Amit, Lover of math. Also, Ph.D. • Answered August 10 Whenever you have any function [math]g(x)[/math] on some set, and you're wondering whether there's an [math]f[/math] on that same set with [math]f(f(x))=g(x)[/math], and you don't care about continuity, differen... Read more » 223 13   Craig Bailey, studied at School for Idiots • Posted May 8 An Englishman, a Frenchman, and an Asian man are work colleagues who decide to go on a fishing trip. The Englishman takes charge and says, "I'll bring the fishing gear & bait, Pierre, you get the b... Read more » 232 32 Read more in your feed

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