Before we can talk about "first-fit vs best-fit", we must earn every word the parent note leaned on: cell, address, block, hole, base + length, the set symbol{…}, size∣hi∣, the requests, the inequality≥, and leftoverH−s. We build each from a picture.
Why the topic needs it. Every later idea — "a block at base B", "a hole from address 200 to 400" — is just a range of these numbered boxes. If you cannot see the ruler of addresses, none of the (base, length) language makes sense. The address is the coordinate system of memory.
Why "contiguous" (unbroken) matters. A program expects its memory to be one straight stretch so it can walk from cell to cell by simple counting (B, then B+1, then B+2...). If the OS gave it two separate pieces, address B+5 might land in someone else's memory. That single word — contiguous — is the entire reason placement is hard.
Why the topic needs it. The whole game is: a program asks for room, and the OS must find a hole big enough. The parent note's "Swiss cheese" picture is exactly figure s03 — filled blocks (busy) alternating with holes (free). The placement rules are all recipes for choosing which hole.
Why this notation. We need to talk about "all the holes" without knowing in advance how many there are. The subscript lets us say general things like "for every hole hi" instead of writing A,B,C,D,E by hand. It is bookkeeping shorthand, nothing more.
Why an inequality and not equals. Requests almost never match a hole exactly. We do not demand a perfect-size hole; we demand a big-enough one, then cut the piece we need. The ≥ captures exactly that "big enough" idea — the single most-used test in the whole topic.
Why this single formula is the heart of the topic. Every placement rule is judged by the leftover it creates. Best-fit tries to make H−ssmall (tight fit); worst-fit tries to make H−slarge (reusable chunk). The subtraction H−s is literally the number that first-fit, best-fit, and worst-fit argue about.
Why both matter. These two words name the failure modes the placement rules fight over. See Fragmentation for the full treatment; here we only need to recognise them by picture: external = wasted between blocks, internal = wasted inside a block.
Read top to bottom: the address ruler makes blocks meaningful, blocks make holes meaningful, holes gather into a free list, the size bars let us test ∣hi∣≥s, that test plus the leftover H−s drive the placement rules — and the leftovers pile up into fragmentation. Now the parent note (parent topic) reads as plain English.