Favourite Mathematical Functions & Equations

[ebola?]

I know fuck all about math, but I'm partial to:

People have expressed this in other forms, but:

e^(pi*i) = -1.

makes it look like math is playing silly jokes on us.

ebola

 

[Kid B]

yeah ebola, the derivative of sinx is cosx
jokes...or elegance

 

[spacelord]

yeah, pi is pretty badass
are there more rational or irrational numbers? there is some proof..

rational numbers are countable, whereas irrational ones are not.

 

[ebola?]

>>
are there more rational or irrational numbers? there is some proof..>>

This will be obvious to the math people, but there are different kinds of infiniti.
Also, infiniti is more rigorously a property of some sets (or the sum of the elements contained) rather than a number.

ebola

 

[felix]

uhh... an infiniti is a type of car, dude. 8)

 

[INFaMaS]

Also, infinity is more rigorously a property of some sets rather than a number.

A set is called infinite if it is in correspondence with a proper subset of itself

The naturals: N = {0,1,2,3,4,...} are infinite because: consider a proper subset S = {1, 2,3,4,5...} of N Clearly, We may be define the set isomorphism f:N --> S via f(n) = n + 1. This function is one-to-one and onto, so N is infinite.

The reals R are infinite, because, consider the subset of positive reals, R+, of R. Now consider the function f:R --> R+ via f(x) = e^x. This is also an isomorphism, so R is infinite.

That is really what infinite means.

 

[11abc11]

I have a fondness for the Cycloid

X=r(t-sint)
Y=r(1-cost)

 

[princess.jessa]

group theory does it for me.

 

[Psyduck]

Algebraic Geometry

 

[PGTips]

yeah, pi is pretty badass
are there more rational or irrational numbers? there is some proof..

There are 'more' irrational numbers than there are rational numbers. Rationals are countable, they have a cardinality of Aleph-Null, while the Irrationals are the Reals minus the rationals and since the cardinality of the Reals is Aleph-One, you have that the cardinality of the irrationals is Aleph-One.

also sin(1/x), as when x approaches 0 it starts bugging out

Ah, good old topologist's sine curve.

Algebraic Geometry

Yep, ideals and the GTZ algorithm rock.

I'd go with the Euler-Lagrange equations myself. It's not a function per-say but it is a functional.

 

[branflakes]

 

[Beenhead]

PV=nRT Come on!

keq= k[A]^x^y/ [AB]^x+y

 

[INFaMaS]

There are 'more' irrational numbers than there are rational numbers. Rationals are countable, they have a cardinality of Aleph-Null, while the Irrationals are the Reals minus the rationals and since the cardinality of the Reals is Aleph-One, you have that the cardinality of the irrationals is Aleph-One.

Actually, claiming that the cardinality of the Reals is Aleph-1 is equivalent to the Continuum Hypothesis! I don't think that is what you meant, hehe. The cardinality of the reals is typically referred to as "c" or sometimes 2^(Aleph-0).

Ah, good old topologist's sine curve

Technically, the topologist's sine curve is { x X sin(1/x) | 0 < x <= 1} U 0 X [-1,1] as it is important that we consider the closure of the graph so you can show neat things such as the set not being path connected and whatnot.

 

[ntype]

...nice, Dead_Flowers
what else you got?

yeah blatantly euler. its the cornerstone of everything it seems!

 

[Avporx]

Q = pi. its the secret to time travel. i found this out on acid :D

 

[PGTips]

Actually, claiming that the cardinality of the Reals is Aleph-1 is equivalent to the Continuum Hypothesis! I don't think that is what you meant, hehe. The cardinality of the reals is typically referred to as "c" or sometimes 2^(Aleph-0).

True, though clearly I'm working in a system where I'm taking the Continuum Hypothesis to be true

Technically, the topologist's sine curve is { x X sin(1/x) | 0 < x <= 1} U 0 X [-1,1] as it is important that we consider the closure of the graph so you can show neat things such as the set not being path connected and whatnot.

Speaking of which, what's the difference between arc connected and path connected. I was reading Nakahara a few years ago and it said they are the same except for some obscene counter examples. Given the book's title is "Geometry, Topology and Physics" it didn't go into the counter examples because for us physicists they aren't relevant.

Sorta reminds me of the one where you construct the Reals but have two origins, making it look like ------:-------- if you see what I mean. Every open set is the same as an interval in R but it's inequivalent to R overall.

This is why I'm not a pure mathematician. In my 1st and 2nd years every time I came up with a 'proof' for an example sheet question and said it outloud to friends one of them would come up with some horrific counter example which I'd never even considered.

Damn pedants!

 

[Thorz]

How does one come to see and appreciate beauty in mathematical functions?

 

[Rogue Robot]

How does one come to see and appreciate beauty in mathematical functions?

by learning their purpose and how they work.

for instance: the witch of agnesi

wiki of witch of agnesi with animations.

 

[imakickassninja]

here is a natural fractal

i love fractalllsss

 

[I am shpongled]

pi = e^(-i)