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Ad infinitum is a Latin
Latin

Latin is an Italic language, historically spoken in Latium and Ancient Rome. Through the Military history of the Roman Empire, Latin spread throughout the Mediterranean and a large part of Europe....
 phrase
List of Latin phrases

This page lists direct English language translations of common Latin phrases, such as veni, vidi, vici and et cetera. Some of the phrases are themselves translations of List of Greek phrases, as Greek language rhetoric and literature were highly regarded in ancient Rome when Latin rhetoric and literature were still maturing....
 meaning "to infinity
Infinity

Infinity comes from the Latin infinitas or "unboundedness." It refers to several distinct concepts – usually linked to the idea of "without end" – which arise in philosophy, mathematics, and theology....
."

In context, it usually means "continue forever, without limit" and thus can be used to describe a non-terminating process, a non-terminating repeating process, or a set of instructions to be repeated "forever", among other uses. It may also be used in a manner similar to the Latin phrase "et cetera
Et cetera

Et cetera is a Latin expression that means "and other things," or "and so forth." It is taken directly from the Latin expression which literally means "and the rest " and is a transliteration of the Greek language "?a? ?te?a" ....
" to denote written words or a concept that continues for a lengthy period beyond what is shown.






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Ad infinitum is a Latin
Latin

Latin is an Italic language, historically spoken in Latium and Ancient Rome. Through the Military history of the Roman Empire, Latin spread throughout the Mediterranean and a large part of Europe....
 phrase
List of Latin phrases

This page lists direct English language translations of common Latin phrases, such as veni, vidi, vici and et cetera. Some of the phrases are themselves translations of List of Greek phrases, as Greek language rhetoric and literature were highly regarded in ancient Rome when Latin rhetoric and literature were still maturing....
 meaning "to infinity
Infinity

Infinity comes from the Latin infinitas or "unboundedness." It refers to several distinct concepts – usually linked to the idea of "without end" – which arise in philosophy, mathematics, and theology....
."

In context, it usually means "continue forever, without limit" and thus can be used to describe a non-terminating process, a non-terminating repeating process, or a set of instructions to be repeated "forever", among other uses. It may also be used in a manner similar to the Latin phrase "et cetera
Et cetera

Et cetera is a Latin expression that means "and other things," or "and so forth." It is taken directly from the Latin expression which literally means "and the rest " and is a transliteration of the Greek language "?a? ?te?a" ....
" to denote written words or a concept that continues for a lengthy period beyond what is shown. Examples include:

  • "The sequence 2, 4, 6, 8, 10 ... continues ad infinitum."
  • "The perimeter of a fractal
    Fractal

    A fractal is generally "a rough or fragmented Shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity....
     may be iteratively drawn ad infinitum."
  • The 17th century writer Jonathan Swift
    Jonathan Swift

    Jonathan Swift was an Anglo-Irish satire, essayist, political pamphleteer , poet and cleric who became Dean of St. Patrick's Cathedral, Dublin, Dublin....
     mocked the idea of self-similarity
    Self-similarity

    In mathematics, a self-similar object is exactly or approximately similarity to a part of itself . Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales....
     in natural philosophy with the following lines in his poem 'On Poetry: A Rhapsody':


  • The Victorian era
    Victorian era

    The Victorian Era of the United Kingdom of Great Britain and Ireland was the period of Victoria of the United Kingdom reign from June 1837 to January 1901....
     mathematician Augustus De Morgan expanded on this with a similar verse

See also

  • The song that never ends
    The Song That Never Ends

    "The Song That Never Ends" is a self-reference and infinite recursion children's song. The song is a single verse long, written in an infinite-loop motif in a march style, such that it naturally flows in a cyclical fashion, repeating the same verse over and over....
  • Turtles all the way down
    Turtles all the way down

    "Turtles all the way down" refers to an infinite regression belief about cosmology, the nature of the universe. The analogy has similarities to some ancient beliefs that the world is borne through the universe on the back of one or more enormous animals , though these myths do not necessarily include an infinity aspect or multiple/endless lay...
  • Recursion
    Recursion

    Recursion, in mathematics and computer science, is a method of defining Function in which the function being defined is applied within its own definition....
  • Self-reference
    Self-reference

    Self-reference is a phenomenon in natural language or formal languages consisting of a Sentence or formula referring to itself directly, or through some intermediate sentence or formula, or by means of some Semantics encoding....
  • Induction
    Induction

    Most common meanings * Inductive reasoning, used in science and the scientific method* Mathematical induction, a method of proof in the field of mathematics...