What is the definition of infinity?

Question

What is the definition of infinity, mathematically, philosophically?

Answer 1

In general, infinity is the quality or state of endlessness or having no limits in terms of time, space, or other quantity. In mathematics, infinity is the conceptual expression of such a "numberless" number. It is often symbolized by the lemniscate (also known as the lemniscate of Bernoulli), which looks something like the numeral 8 written sideways
Infinity in cosmology
An intriguing question is whether actual infinity exists in our physical universe: Are there infinitely many stars? Does the universe have infinite volume? Does space "go on forever"? This is an important open question of cosmology. The two-dimensional surface of the Earth, for example, is finite, yet has no edge. By walking/sailing/driving straight long enough, you'll return to the exact spot you started from. The universe, at least in principle, might have a similar topology; if you fly your space ship straight ahead long enough, perhaps you would eventually revisit your starting point.

infinity - time without end
Synonyms: eternity
Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life.
In philosophy, infinity can be attributed to space and time.

Seek the Infinite, for that alone is Joy unlimited, imperishable, unfailing, self-sustaining, unconditioned, timeless. When you have this joy, human life becomes a paradise; the light, the grace, the power, the perfections of that which is highest in your inner consciousness, appear in your everyday life. - Swami Omkarananda

Whenever we encounter the Infinite in man, however imperfectly understood, we treat it with respect. Whether in the synagogue, the mosque, the pagoda, or the wigwam, there is a hideous aspect which we execrate and a sublime aspect which we venerate. So great a subject for spiritual contemplation, such measureless dreaming -- the echo of God on the human wall! - Victor Hugo

While many people are trying to be in tune with infinite, what they really are is in tune with the indefinite. - Eric Butterworth

The poetic notion of infinity is far greater than that which is sponsored by any creed. - Joseph Brodsky

Offer unto me that which is very dear to thee -- which thou holdest most covetable. Infinite are the results of such an offering. - Bhagavad Gita

There is no more steely barb than that of the Infinite. - Charles Baudelaire
Infinity is indefinable; however, most subtly, the effects of Infinity are discernable by a careful examination of the most fundamental manifestations of all that which exists.

Answer 2

infinity---can be defined in different ways such as:

mathematically -
As for the name of the symbol, it is simply "infinity." It has no other fancy name, and in fact has no "official" name. Some do refer to it as lazy eight, & some call it lemniscate. As far as lemniscate goes, it is actually d name of a mathematical system that just looks like d symbol for infinity. The symbol itself was introduced by mathematician John Wallis in 1655 when he wrote "De sectionibus conicis." The symbol was supposedly borrowed from a Roman symbol for 1 000 & was declared to represent infinity...

philosophically:
*Infinity isn't a number, & its not a thing. It is more appropriately, an idea. Infinity stands for d "never endingness" aspect of some things. We know that numbers never end, but there is no number labeled as "infinity". Rather, we use the word infinity to describe d nature of numbers; they never end. The same is also true for anything that is "infinite" by nature.

Answer 3

What your dad seems to be attempting to assert is that an extremely small quantity divided with the aid of an extremely super quantity, regardless of the words changing between time and length. hardship together with his definition comes up on 2 counts, however. a million. in case you're taking an extremely small quantity and divide it with the aid of an extremely great quantity, the quotient is going to be quite small... till he's conversing approximately "infinity" as some thing infinitely small (rather than infinitely super). 2. A millisecond is a measurable unit of time. a easy 12 months is a measurable unit of length. in case you carry out any operation on measurable (nonzero) quantities, the consequence would be a finite quantity, regardless of if quite small or quite super... neither of which comes on the brink of infinity. Infinity is immeasurable. it rather is not a quantity. some thing infinitely super is bigger than any quantity, and a few thing infinitely small is nearer to 0 than something could be. that's what makes it considered one of those puzzling thought... maximum human beings think of by using fact "infinity" is taught in a math classification that it would desire to be a quantity, and it rather is not.

Answer 4

The accepted way to define infinity is through the "axiom of infinity"(There is a set N, such that the empty set is in N and such that whenever x is a member of N, the set formed by taking the union of x with its singleton {x} is also a member of N) [1] in ZFC[2] which is the accepted axiomatization of set theory.

P.S. I know this is not satisfying, but it EXTREMELY formal and very useful.

Answer 5

Infinity would be the number of times that one could go around a circle.

Answer 6

If i remember my maths A-level correctly. Infinity was equal to 1 divided by 0.

Answer 7

The Bush Dynasty...it seems.

Answer 8

Endless! something that doesnt have an end

Answer 9

Endless and forever!!

Answer 10

never ending