How would I show the following have a bijection. Which is one to one and onto ofcourse.

$\mathbb{Z}\rightarrow \mathbb{N}$

I know I need to find a function. But I do not see the pattern that makes integer go to natural. I already did this problem from natural to integer but now I want to see it done this way.

I have listed some numbers

$,..,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,..$

$1,2,3,4,5,6,7,8,9,10,11,12,13,14,.$


Question: Why Have The System Builder Market Not Migrated to the BTX Form Factor from ATX yet?
Answer: There seems to be insufficient drive to make the change.

There was some noise that BTX offered better component layouts (speed) and airflow for hotter components, but when you look at the requirements for case manufacturers to change their case designs (or as some manufacturers attempted - offer convertible designs), motherboard manufacturers to change their layouts, etc... it's not enough benefit to drive the costs and make the change.