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revo74
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Is infinity a mathematical concept or a number? Please elaborate. Is there any debate over this topic or is there a consensus amongst academia?
uperkurk said:Infinity is never classes as a number. Take for example
Infinity - Infinity = ?
You can't add, subtract, divide or multiply by infinity.
uperkurk said:Infinity is never classes as a number. Take for example
Infinity - Infinity = ?
You can't add, subtract, divide or multiply by infinity.
HallsofIvy said:We can't give a complete answer to that until you define what you mean by "number".
If you are referring to the ordinary "real number system" (and its subsets) then, no, "infinity" is not a number.
There are, however, ways of extending the real number system, one of which adds 'infinity" and "negative infinity" as numbers. Caution- the usual laws of arithmetic do not generally hold in such a system- you still can't say "infinity - infinity= 0".
revo74 said:Didn't Hilbert and Cantor believe infinity was a number?
If you extended the real number system to include infinity then what isn't it indeed classified as a number?
revo74 said:Is infinity a mathematical concept or a number? Please elaborate. Is there any debate over this topic or is there a consensus amongst academia?
revo74 said:Didn't Hilbert and Cantor believe infinity was a number?
If you extended the real number system to include infinity then what isn't it indeed classified as a number?
jreelawg said:I say it's not a number because it's not quantifiable.
uperkurk said:Extending the number system to include infinity would ultimately give infinity a value. Infinity does not have any direct value so it is not a number.
SteveL27 said:How about pi = 3.14159265... continuing forever. Is it quantifiable? Is it a number?
uperkurk said:9 followed by ∞ 9's or 1 followed by ∞ 1's?
Number Nine said:What is the value of aleph null? Methinks a good course in abstract algebra would clear up a lot of these restricted notions of what constitutes a number.
uperkurk said:Regardless of how people try to justify infinity, the bottom line is if something goes on forever it can never have a number, a value yes but not a number
coolul007 said:Don't we use infinity to define a set of numbers, as in a series, to reach a limit or it is limitless. Isn't the underlying premise of Calculus infinite members of a set?
HallsofIvy said:Yes, but that has nothing to do with the question of whether infinity "is a number or a concept".
micromass said:The thing is that there is no such thing as a "number" in mathematics. We do have
- Rational numbers
- Real numbers
- Surreal numbers
- Transfinite numbers
- p-adic numbers
and many more. Some of these systems allow some form of infinity. But mathematicians never speak of just numbers.
Number Nine said:You seem to be treating "number" as synonymous with "real number"; which is to say, "something you can count with". Number systems are just algebraic structures; the elements of those structures are called numbers, whatever they may be. It may disturb you to know that every real number is actually a collection of intervals on the rational number line (a classic construction of the real numbers: Dedekind cuts). We call each of these intervals a real number because it's convenient, and they behave the way we expect real number to behave.
Do you object to the existence of cardinal numbers? Ordinal numbers?
coolul007 said:However, with the exception of complex numbers, all "numbers" have a fixed location on a number line infinity does not. So, a concept of limitlessness.
revo74 said:I was told that Cantor possibly Hilbert as well, considered infinity to be a number. Is this true?
revo74 said:So infinity is a number then?
revo74 said:Is there any official mathematical dictionaries that define infinity? It seems to me that there are various views on this topic. Is there any authority that decides such things?
Hitarth said:Infinity is not a real number then why sometime it is domain or range of a real function?