The simplest way to answer this question would be to identify the properties of each set (i.e. Real, Complex, and Integers). Then observe the properties of infinity and see what possible sets infinity could exist in.
If you can list any known properties of infinity I would be super impressed. Other then its infinite... I was thinking. Its hard to say but its a finite idea. Can it be called a finite number? Other words, do we have any idea of its value?
Infinity is not a number, rather it is a placeholder or an idea. This being said i dont believe that infinity is rational, irrational etc. It doesnt fit definitively into any of those categories. Its kind of in its own category.
So I was able to find a website not very up scale web site but I was able to find some things on the site that helped me come to a starting point on where to begin. I will post the link below and take a look at it guys and let me know what you all think so far my idea is thinking of it as a number, this is not correct, but It gave me an idea to think from, the more i thought about it i began to see that it is a little like Pi (3.14...) it continues on for ever, conclusion so far it is non-real, but is also still rational. http://www.mathsisfun.com/numbers/infinity.html
It isn't a number because as your website said because it is not reachable nor does it grow. You and me talked about the universe when discussing infinity. We will never reach the edge of the universe because it is infinite to our knowledge. Planets and systems are moving at an increasing rate towards the edge yet they will never actually reach the edge. We can make any number increase towards infinity but it will never reach infinity. Just like the difference quotient. H can never equal 0 but it can always get closer.
AH! Your connection here to the difference quotient is critical! "It can always get closer..." is central to the "limit concept" and this is one of the key concepts of calculus! The mathematician Bertrand Russell classified the Limit concept as THE most important idea of 20th century mathematics.
@Julian the thing is infinity has to belong to a number set of sorts. If infinity is used to describe a vast amount of numbers that theoretically never stop expanding. And the numbers that are found within infinity all belong to a number set. This means infinity should be able to find its way into a number set.
I also think that it has no specific value because it is a concept, and since it is a concept I believe instead of the families/categories containing infinity, infinity contains them.
I see it as an idea. Unobtainable yet we understand the concept. We can never reach infinity because it is the concept of always increasing.
ReplyDeleteSo Brian is asking if we can include infinity as a member of the set of Reals, for instance? An interesting question....
ReplyDeleteThe simplest way to answer this question would be to identify the properties of each set (i.e. Real, Complex, and Integers). Then observe the properties of infinity and see what possible sets infinity could exist in.
ReplyDeleteIf you can list any known properties of infinity I would be super impressed. Other then its infinite... I was thinking. Its hard to say but its a finite idea. Can it be called a finite number? Other words, do we have any idea of its value?
DeleteInfinity is not a number, rather it is a placeholder or an idea. This being said i dont believe that infinity is rational, irrational etc. It doesnt fit definitively into any of those categories. Its kind of in its own category.
ReplyDeleteSo I was able to find a website not very up scale web site but I was able to find some things on the site that helped me come to a starting point on where to begin. I will post the link below and take a look at it guys and let me know what you all think so far my idea is thinking of it as a number, this is not correct, but It gave me an idea to think from, the more i thought about it i began to see that it is a little like Pi (3.14...) it continues on for ever, conclusion so far it is non-real, but is also still rational.
ReplyDeletehttp://www.mathsisfun.com/numbers/infinity.html
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DeleteIt isn't a number because as your website said because it is not reachable nor does it grow. You and me talked about the universe when discussing infinity. We will never reach the edge of the universe because it is infinite to our knowledge. Planets and systems are moving at an increasing rate towards the edge yet they will never actually reach the edge. We can make any number increase towards infinity but it will never reach infinity. Just like the difference quotient. H can never equal 0 but it can always get closer.
ReplyDeleteWhen do numbers grow I've always thought they were a set value?
DeleteAH! Your connection here to the difference quotient is critical! "It can always get closer..." is central to the "limit concept" and this is one of the key concepts of calculus! The mathematician Bertrand Russell classified the Limit concept as THE most important idea of 20th century mathematics.
ReplyDelete@Julian the thing is infinity has to belong to a number set of sorts. If infinity is used to describe a vast amount of numbers that theoretically never stop expanding. And the numbers that are found within infinity all belong to a number set. This means infinity should be able to find its way into a number set.
ReplyDeleteI also think that it has no specific value because it is a concept, and since it is a concept I believe instead of the families/categories containing infinity, infinity contains them.
ReplyDelete