Invertible: meaning, definitions and examples
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invertible
[ ɪnˈvɜːrtəbl ]
mathematics, functions
An invertible function is a function that has an inverse. This means that for each output of the function, there exists a unique input that produces that output. In practical terms, an invertible transformation can be reversed, leading to the original state or value.
Synonyms
backtrackable, reversible
Examples of usage
- The function f(x) = 2x is invertible.
- An invertible matrix can be used to solve linear equations.
- For a function to be invertible, it must be one-to-one.
general use
Invertible also describes an object that can be flipped or changed into its opposite form. This pertains to physical objects or abstract concepts that can be undone or altered in a reversible manner.
Synonyms
Examples of usage
- The coat was designed to be invertible.
- Some garments are made to be invertible for fashion versatility.
- An invertible decision allows re-evaluation later.
Etymology
The term 'invertible' stems from the late 19th century, derived from the Latin 'invertibilis,' which combines 'in-' meaning 'not' and 'vertere' meaning 'to turn.' Thus, the original essence of the word relates to the ability to turn back or reverse a process or operation. In mathematical context, the term has become particularly important, helping to establish a foundation in discussions regarding functions and matrices. The adoption of 'invertible' in mathematics aligns with the broader philosophical discussion on reversibility and conservation, extending its meaning beyond mathematics into realms such as physics and information theory.