What is the concept of infinity in mathematics?

[Hamza Abbasi]

Infinity is not a real number right? Then where do infinity stand (complex no?) . Why infinity is not a real number , I thought of it as a very very big real number! Ignore my poor communication skills.

 

[blue_leaf77]

I'm not a mathematician, but I found this site interesting https://www.mathsisfun.com/numbers/infinity.html.
Also, many calculations in physics which involves infinity, in reality is not exactly true as for instance our universe and the time continuum are finite.

 

[HallsofIvy]

No, infinity is NOT a "very very big real number". All the real numbers have the property that, for any real number, x, x+ 1 is even larger. There are a variety of ways of defining positive and negative "infinity" geometrically, for example, in such a way that the set of all real numbers and positive and negative "infinity" is 'homeomorphic' to the interval [a, b] for any real numbers, a, b, a< b. But one can also define a single "infinity" so that the set of all real numbers and this one "infinity" is homeomorphic to a circle in a plane. Once can define "hyper-real" numbers that include notions of "infinite numbers" as well as "infinitesimal numbers" that satisfy certain arithmetic rules. But in none of those cases can you do "regular" arithmetic, with the usual arithmetic rules for the real numbers, with "infinity".

 

[aikismos]

It's better to think of infinity as the conceptual process of 'going on forever'. Sometimes you'll hear it called an extension to the reals in more formal systems so that it can be used when doing math. Most people get their first taste of infinity young $(1, 2, 3, 4, ... )$, but the lemniscate isn't usually used until the end of high school in precalculus classes where the notion of the difference quotient and limit are introduced.

 

[Ssnow]

In mathematics $\infty$ is just a symbol that mathematicians use according some rules, what is the concept of infinity? This the difficult question ...