The title says it all. I was hoping the community could check me on my understanding of translating the following sentence to an inequality:
y is at least 2 units from pi
I'm thinking the following inequality is an accurate translation:
[edited] $$ |y-\pi|\ge2 $$
Distance at least 2 means the difference between the numbers is 2 or larger.
Suppose $y > \pi$, then we would translate the sentence to $y - \pi \geq 2$.
Suppose $\pi > y$, then we would translate the sentence to $\pi - y \geq 2$ or equivalently $-(y - \pi) \geq 2$.
The two expressions can be joined together as: $$|y - \pi| \geq 2$$
In short, we can consider $|a-b|$ as a distance function between the values $a$ and $b$.