Math Wiki

Infinity, a concept widely used in mathematics and physics which is not a number, means "without end" or "without bounds", comes from the Latin word "infinitas" meaning "without bounds"

Infinity is usually treated like a number as it is used to denote numbers of things, but it is not a real number. If a number system includes infinitesimals, often expressed as 1/ then 1 over it would become a number greater than any other number.

In the late 19th century to the early 20th century, Georg Cantor made many thoughts about infinity or infinite sets. He developed a theory stating that there are infinite sets of different sizes.



The first cases of infinity were by Zeno of Elea, at around 450 BC. Also called the developer of the dialectic by Aristotle, the Italian philosopher was very famous for his paradoxes which were called "immeasurably subtle and profound" by Bertand Russell, a British Logician.

Like Aristotle's view, the Greeks want to differentiate the actual infinity from the potential infinity. So, instead of saying that there are an infinite number of primes, Euclid says that there are more primes than any collecten today. (Elements, Book IX, Proposition 20).

Indian (taken from Wikipedia)

The Isha Upanishad of the Yajurveda (c. 4th to 3rd century BC) states that "if you remove a part from infinity or add a part to infinity, still what remains is infinity".

The Indian mathematical text Surya Prajnapti (c. 400 BC) classifies all numbers into three sets: enumerable, innumerable, and infinite. Each of these was further subdivided into three orders:

  • Enumerable: lowest, intermediate, and highest
  • Innumerable: nearly innumerable, truly innumerable, and innumerably innumerable
  • Infinite: nearly infinite, truly infinite, infinitely infinite

In the Indian work on the theory of sets, two basic types of infinite numbers are distinguished. On both physical and ontological grounds, a distinction was made between asaṃkhyāta("countless, innumerable") and ananta ("endless, unlimited"), between rigidly bounded and loosely bounded infinities.


The symbol of infinity is .


Since infinity is not a number, it cannot be used in arithmetic and algebraic operations.