onto

Onto is a preposition and an adverb in English. It conveys movement toward and onto a surface, or the action of landing on and staying on that surface. It is used with verbs of motion and with phrases describing destination or position, as in “The cat jumped onto the sofa” and “She stepped onto the platform.”

Word usage distinctions: In many contexts of motion, onto indicates arriving on top of something. In phrases that denote progression to another task, the two-word form “on to” is often used, as in “She went on to explain.” Some style guides advise using onto for physical movement and on to for sequential transitions, but practice varies.

Mathematics: In mathematics, onto is short for surjective. A function f: A -> B is onto (surjective) if every element of B has a preimage in A; equivalently, the range of f equals B. Examples: The function f(x) = x^3 is onto R; f(x) = e^x maps R onto (0, ∞) and is not onto R.

Etymology: The term originates from the fusion of “on” and “to” in Old English and Middle English, transitioning to a single word by the modern period. It is etymologically a literal combination indicating movement onto a surface.