0 like 0 dislike
0 like 0 dislike
What is your favorite function?

56 Answers

0 like 0 dislike
0 like 0 dislike
The function that maps rationals to 1 and irrationals to 0
0 like 0 dislike
0 like 0 dislike
∅:∅→∅
0 like 0 dislike
0 like 0 dislike
I found myself pretty fascinated by the gamma function a few months ago... there's something about the extension of factorials to the negative domain that is deeply pleasing to me
0 like 0 dislike
0 like 0 dislike
The determinant (det: M_n(R) -> R) is king.
0 like 0 dislike
0 like 0 dislike
I'm going to cheat and say the Dirac delta. It was my introduction to distributions.
0 like 0 dislike
0 like 0 dislike
Riemann zeta function FTW!
0 like 0 dislike
0 like 0 dislike
Weierstrass function
Continuous everywhere, but not differentiable anywhere
by
0 like 0 dislike
0 like 0 dislike
f(x) = x

Identity function is the best function. Change my mind.
0 like 0 dislike
0 like 0 dislike
Let G be a group, with g in G.

The function G-> G that maps x to gx is my favorite.

The fact that it is bijective (therefore a permutation of G) is the reason why every group is (subgroup of) a permutation group (aka Cayley's Theorem).

That kind of represents Group Theory to me.
0 like 0 dislike
0 like 0 dislike
Recall that the Cantor set `K` is the space of infinite bit sequences, topologized as the product of countably many copies of `2`. Let `L` be the space of arbitrary functions `K -> 2`, and let `N*` be the one-point compactification of `N`, i.e., the closure of `N` as a subset of the real projective line. Define a map `w : L -> N*` as follows:

* If `f : K -> 2` is continuous, then `w(f)` is the smallest natural number `n` such that the value of `f(x)` is completely determined by the first `n` bits of `x`. (It is easy to see that `f` is continuous if and only if such an `n` exists.)

* If `f : K -> 2` isn't continuous, then `w(f)` is infinity.

Today, my favorite function is `w`.

**EDIT:** Fixed typo.

Related questions

0 like 0 dislike
0 like 0 dislike
16 answers
TEATROCLASICO asked Jun 21
Fellow mathers: Are you proud of your (math-related) thesis?
TEATROCLASICO asked Jun 21
0 like 0 dislike
0 like 0 dislike
13 answers
cjruth44 asked Jun 21
Using your own math notation
cjruth44 asked Jun 21
0 like 0 dislike
0 like 0 dislike
26 answers
vickywong710 asked Jun 21
Non-native English speakers: What does your blackboard look like?
vickywong710 asked Jun 21
0 like 0 dislike
0 like 0 dislike
35 answers
nobodyeatsalone asked Jun 21
What was the average percentage of people that failed a course at your university?
nobodyeatsalone asked Jun 21
0 like 0 dislike
0 like 0 dislike
14 answers
KidConrad asked Jun 21
What is your favorite hypothesis that seems to hold only if you consider the first, say, million numbers?
KidConrad asked Jun 21

29.6k questions

121k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!