33 questions linked to/from 'Obvious' theorems that are actually false
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### Things you've believed for a long time were true, but are false in reality [duplicate]

Do you have any things (mathematical statements, statements about mathematics) you've believed for a long time were true, but now with enough mathematical knowledge you realize were wrong? For example,...
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### What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) [closed]

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's Lament,...
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### What are some counter-intuitive results in mathematics that involve only finite objects?

There are many counter-intuitive results in mathematics, some of which are listed here. However, most of these theorems involve infinite objects and one can argue that the reason these results seem ...
### False beliefs about Lebesgue measure on $\mathbb{R}$
I'm trying to develop intuition about Lebesgue measure on $\mathbb{R}$ and I'd like to build a list of false beliefs about it, for example: every set is measurable, every set of measure zero is ...