Grammatical number marks quantification distinctions on nouns and their modifiers. Beyond the familiar singular/plural, languages exhibit dual (exactly two), trial (three), paucal (small quantity), or more complex systems; some languages have no number marking at all or mark it only in specific contexts.
From your work in linguistic typology, you know that languages differ dramatically in how they encode the same conceptual territory. Grammatical number is one of the clearest illustrations: every human language needs to distinguish "one thing" from "more than one thing" in some way, but the grammatical machinery used to do this — and exactly which distinctions it encodes — varies widely across languages.
English belongs to the singular/plural system, the most common type globally. You mark singular with no suffix (cat) and plural with -s or irregular forms (cats, feet). This two-way opposition is so familiar it can feel universal, but it is just one point on a typological spectrum. Many Austronesian and Oceanic languages have a dual number, marking exactly two referents with a distinct morpheme separate from both singular and plural: "the two of us" is encoded in the verb or noun itself, not by combining a number word with a plural. Some languages (Fijian, Larike) extend this with a trial (exactly three) or a paucal (a small, unspecified few — roughly "a handful of"). When a language has a paucal, the "plural" typically means something larger than a small group rather than simply "more than one."
The morphological encoding of number interacts with what you know about inflection from your study of morphological structure. Number marking can appear on nouns (the most common locus), on adjectives that agree with nouns, on verbs that agree with subjects or objects, or on multiple elements simultaneously. Arabic, for instance, has singular, dual, and plural, with all three forms potentially triggering different agreement patterns on adjectives and verbs. Some languages exhibit number neutrality for certain noun classes: Japanese nouns, for example, bear no number morphology at all — context and explicit quantifiers carry the weight. This doesn't mean Japanese speakers can't distinguish one from many; it means the grammar does not grammaticalize that distinction in the same place English does.
The typological question underlying all of this is: which distinctions does a grammar obligatorily encode? English speakers must always decide whether to say "cat" or "cats" — number is obligatory. Arabic speakers must choose among singular, dual, and plural. Japanese speakers make this choice with quantifiers and context, not morphology. Each system reflects a different answer to how the language packages quantificational information into its morphological and syntactic machinery. Understanding these systems as options within a typological space, rather than as variations on the English model, is the key conceptual move that your study of typology and morphology has prepared you to make.