Proposition
24
[20B] Let \(A β β\) not empty, let \(lβββͺ\{ -β\} \); the following properties apply:
|
\(\inf A β₯ l\) |
\(β xβ A,xβ₯ l\) |
|
\(\inf A {\lt} l\) |
\(β xβ A,x{\lt}l\) |
|
\(\inf A {\gt} l\) |
\(β h{\gt}l , β xβ A,xβ₯ h\) |
|
\(\inf A β€ l\) |
\(β h{\gt}l, β xβ A,x{\lt} h\) |
If \(lβ -β\) then also we write (substituting \(h=l+\varepsilon \))
|
\(\inf A {\gt} l\) |
\(β \varepsilon {\gt}0 , β xβ A,xβ₯ l+\varepsilon \) |
|
\(\inf A β€ l\) |
\(β \varepsilon {\gt}0, β xβ A,xβ€ l+\varepsilon \) |