What is the concept of infinity in mathematics?

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In summary, the conversation discusses the concept of infinity and its role in mathematics and physics. It is not a real number and cannot be treated as such in calculations. There are various ways to define and conceptualize infinity, including as a process of going on forever and as an extension of the real numbers. The conversation also mentions the use of infinity in the difference quotient and limit in precalculus classes. The concept of infinity is complex and can be difficult to fully understand.
  • #1
Hamza Abbasi
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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.
 
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  • #2
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.
 
  • #3
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".
 
  • #4
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.
 
  • #5
In mathematics ## \infty## is just a symbol that mathematicians use according some rules, what is the concept of infinity? This the difficult question ...
 

1. What is infinity?

Infinity is a concept in mathematics and philosophy that refers to something that has no limit or end. It is often symbolized by the symbol ∞ and is used to represent something that is unbounded or limitless.

2. How is infinity defined in mathematics?

In mathematics, infinity is defined as a concept that represents the idea of something that has no limit or end. It is used to describe the behavior of numbers or quantities that grow without bound, such as in the case of the number line or the concept of infinite series.

3. Is infinity a number?

No, infinity is not considered a number in mathematics. It is a concept that represents something that is unbounded or limitless, and therefore cannot be expressed as a specific numerical value.

4. Can infinity be reached or measured?

No, infinity cannot be reached or measured. It is a concept that describes something that has no limit or end, and therefore cannot be quantified or measured in a tangible way.

5. What is the difference between infinity and infinity plus one?

Infinity plus one is a mathematical concept that is used to explore the properties of infinity. It is not the same as infinity itself, which represents something that has no limit or end. Infinity plus one is simply a way of expressing that there is something beyond infinity, not a specific mathematical quantity.

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