# Infinite vs. Infinity

By Jaxson

• Infinity

Infinity (symbol: ∞) is a concept describing something without any bound, or something larger than any natural number. Philosophers have speculated about the nature of the infinite, for example Zeno of Elea, who proposed many paradoxes involving infinity, and Eudoxus of Cnidus, who used the idea of infinitely small quantities in his method of exhaustion. This idea is also at the basis of infinitesimal calculus.

At the end of 19th century, Georg Cantor introduced and studied infinite sets and infinite numbers, which are now an essential part of the foundation of mathematics. For example, in modern mathematics, a line is viewed as the set of all its points, and their infinite number (the cardinality of the line) is larger than the number of integers. Thus the mathematical concept of infinity refines and extends the old philosophical concept. It is used everywhere in mathematics, even in areas, such as combinatorics and number theory that may seem to have nothing to do with it. For example, Wiles’s proof of Fermat’s Last Theorem uses the existence of very large infinite sets.

The concept of infinity is also used in physics and the other sciences.

Wikipedia

Indefinably large, countlessly great; immense. from 14th c.

Boundless, endless, without end or limits; innumerable. from 15th c.

With plural noun: infinitely many. from 15th c.

Greater than any positive quantity or magnitude; limitless. from 17th c.

Having infinitely many elements.

Not limited by person or number. from 19th c.

Capable of endless repetition; said of certain forms of the canon, also called perpetual fugues, constructed so that their ends lead to their beginnings.

• Infinite (numeral)

Infinitely many.

• Infinite (noun)

Something that is infinite in nature.

• Infinity (noun)

Endlessness, unlimitedness, absence of a beginning, end or limits to size.

• Infinity (noun)

A number that has an infinite numerical value that cannot be counted.

• Infinity (noun)

An idealised point which is said to be approached by sequences of values whose magnitudes increase without bound.

• Infinity (noun)

A number which is very large compared to some characteristic number. For example, in optics, an object which is much further away than the focal length of a lens is said to be “at infinity”, as the distance of the image from the lens varies very little as the distance increases further.

• Infinity (noun)

The symbol ∞.

Wiktionary

limitless or endless in space, extent, or size; impossible to measure or calculate

“the infinite number of stars in the universe”

“the infinite mercy of God”

very great in amount or degree

“he bathed the wound with infinite care”

greater than any assignable quantity or countable number.

(of a series) able to be continued indefinitely.

another term for non-finite

• Infinite (noun)

a space or quantity that is infinite

“beyond the infinite, the space traveller is transformed”

• Infinite (noun)

God

“intimations of the infinite”

• Infinity (noun)

the state or quality of being infinite

“the infinity of space”

• Infinity (noun)

an infinite or very great number or amount

“an infinity of combinations”

• Infinity (noun)

a point in space or time that is or seems infinitely distant

“the lawns stretched into infinity”

• Infinity (noun)

a number greater than any assignable quantity or countable number (symbol ∞)

“the transmission approaches 100% as the frequency tends to infinity”

Oxford Dictionary