/sci/ - Science & Math

[Anonymous No.11528082]

How does one come up with the injective function
[math]f:\mathbb{N} \rightarrow \mathbb{N}\cross\mathbb{N}[\math] shown in the picture?

[Anonymous No.11528406]

>>11528082
[math]f:\mathbb{N} \rightarrow \mathbb{N}\cross\mathbb{N}[/math]

[Anonymous No.11528415]

>>11528406
http://detexify.kirelabs.org/classify.html
Just draw the symbol you are looking for into the square area above and look what happens

[Anonymous No.11528418]

>>11528082
Well you have an infinite square and you want to list them all one by one, without repeating anything and in such a way that every element of the square is listed somewhere. How do you do it in a systematic way? In my opinion, listing them in a diagonal fashion as in your pic related is the most natural way to listen them.
It's just one of the tricks in mathematics that you once learn about and never forget.

[Anonymous No.11528434]

>>11528082
The nth triangular number is n(n+1)/2
Find the largest triangular number, t, that is less than or equal to x-1.
Find the n corresponding to t.
Let r = x-t.
Map x to (n+2-r,r)
You can find n by solving y(y+1)/2 = x-1 then letting n = floor(y)
Use that n to get t.

[Anonymous No.11528527]

>>11528082
What book is this?