# Linked Questions

33 questions linked to/from 'Obvious' theorems that are actually false
0answers
117 views

### 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,...
164answers
49k views

### 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,...
36answers
21k views

### 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 ...
7answers
2k views

### 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 ...
10answers
4k views

I know the higher-math answer to this question, but I'm asking how on Earth to explain it to a bright high school student. Here's the question, paraphrased: “I can see that $\left(1+x+x^{2}+x^{3}+x^{... 6answers 11k views ### Help: rules of a game whose details I don't remember! In a probability course, a game was introduced which a logical approach won't yield a strategy for winning, but a probabilistic one will. My problem is that I don't remember the details (the rules of ... 3answers 2k views ### How does intuition fail for higher dimensions? From this answer: Now, Algebraic Geometry is one of the oldest, deepest, broadest and most active subjects in Mathematics with connections to almost all other branches in either a very direct ... 2answers 13k views ### Who discovered this number-guessing paradox? In this math.se post I described in some detail a certain paradox, which I will summarize:$A$writes two distinct numbers on slips of paper.$B$selects one of the slips at random (equiprobably), ... 6answers 7k views ### Help to understand material implication [closed] This question comes from from my algebra paper:$(p \rightarrow q)$is logically equivalent to ... (then four options are given). The module states that the correct option is$(\sim p \lor q)$. ... 4answers 4k views ### How many smooth functions are non-analytic? We know from example that not all smooth (infinitely differentiable) functions are analytic (equal to their Taylor expansion at all points). However, the examples on the linked page seem rather ... 2answers 3k views ### Must the (continuous) image of a null set be null? Say$E \subset [0,1]$is a null set. Let$f: [0,1] \rightarrow [0,1] $. Do you think$f(E)$is a null set or not? Just being curious. (DEF): A set$A$is null if given any$\epsilon > 0$, there ... 3answers 1k views ### The limit of the derivative of an increasing and bounded function is always$0$? Let$\,f : \mathbb{R} \rightarrow \mathbb{R}$be a infinitely differentiable function that is increasing and bounded. Then is it true that$\lim_{x\to \infty}f'(x)=0$? 2answers 3k views ### Graph of discontinuous linear function is dense$f:\mathbb{R}\rightarrow\mathbb{R}$is a function such that for all$x,y$in$\mathbb{R}$,$f(x+y)=f(x)+f(y)$. If$f$is cont, then of course it has to be linear. But here$f$is NOT continous. Then ... 3answers 8k views ### an example of a continuous function whose Fourier series diverges at a dense set of points Please give me a link to a reference for an example of a continuous function whose Fourier series diverges at a dense set of points. (given by Du Bois-Reymond). I couldn't find this in Wikipedia. 8answers 379 views ### Examples of “transfer via bijection” On some occasions I have seen the following situation: We want find out whether a set of a given cardinality$\varkappa\$ has some property P. If this property is invariant under bijective maps, then ...

15 30 50 per page