Are mathematical constants equivalent to Infinity?

[ajb]

So, the value of Infinity is:

Infinity = 9999999999999999999999999...

.....

 

What do you guys think?

Did we not discuss this already?

(http://www.scienceforums.net/topic/87858-are-mathematical-constants-equivalent-to-infinity/?p=855376)

 

The problem was to make sense of the right hand side. I did that using limits and found that the only way I could really interpret what you wrote is trivial. What is written on the right hand side is not a number.

Edited April 5, 2015 by ajb

[Mr. Astrophysicist]

Did we not discuss this already?

(http://www.scienceforums.net/topic/87858-are-mathematical-constants-equivalent-to-infinity/?p=855376)

 

The problem was to make sense of the right hand side. I did that using limits and found that the only way I could really interpret what you wrote is trivial. What is written on the right hand side is not a number.

Yeah we did, but I did make a little tweak, elucidating that the value is not affected by numbers

[ajb]

Yeah we did, but I did make a little tweak, elucidating that the value is not affected by numbers

You mean 'infinity + 1 = infinity' etc?

 

This one of the axioms of the extended real number line.

 

Anyway, I am very unclear on what you mean by 'value of infinity'. By value I would normally think of some assignment of a real number to a mathematical object, something like an evaluation map. But the property 'infinity +1 = infinity' tells you that you cannot think of infinity as a standard real number. Thus, it has no 'value'. Or do you mean something else by 'value'?

 

Your 999... just seems to be a very inconvenient way of writing [math]\infty[/math].

[studiot]

 

ajb

Thus, it has no 'value'. Or do you mean something else by 'value'?

 

 

 

Just to take up this point a little further.

 

We discussed in your other threads that things in general and infinity in particular have 'properties'.

 

Properties are the means by which things interact with other things.

They are the means by which we can observe and perhaps measure this interaction.

 

Observing one particular property does not in general say anthing about another and different property.

 

With particular regard to infinity.

 

One property is that it can be considered in some sense 'going on forever'.

This property is what we talk about when we take limits and think of the relationship between infinity and ordinary numbers.

 

The idea that if N is an integer, there is always an integer (N+1) bigger than N and you can go on adding N forever.

That is you never get to the end of the process.

 

But this is an inconvenient property and for some purposes we consider the entire sequence is finished and present.

We do this for projective geometry - the point or line at infinity is always there, not somethign we can never reach.

We do this for the different properties that ajb mentioned on the extended number line.

 

We do this for a whole theory of different infinities or different properties of infinity.

 

These properties are not necessarily transferable so don't mix them up.

[petrushka.googol]

limit (a -> infinity) / (b-> infinity) = some finite number (possibly unity)

 

limit ((a + 1) / (b + 1)) = some finite number

 

if limit (some number -> infinity i.e. ~infinity) is finite....then why infinity / infinity is undefined.

 

Rationale is : infinity - delta / infinity - delta is still finite.

 

Then why this anomaly ?

[studiot]

 

p.g

if limit (some number -> infinity i.e. ~infinity) is finite....then why infinity / infinity is undefined.

 

Who said it was undefined?

 

It may be that it is not calculable.

That would be the case with your example since we don't know what a and b are and their relationship.

 

'Some number' is correct, but that number is not fixed since there are many different infinities and 'some number' will be different depending upon the circumstances.

[ajb]

Infinity divided by infinity is usually left undefined as it cannot be interpreted uniquely. It depends on how you take the limits. Again, you should not think of infinity as a real number, it does not obey all the rules including the one about multiplicative inverses.

Edited April 7, 2015 by ajb

[hypervalent_iodine]

!

Moderator Note

merging with the existing thread. Mr Astrophysicist, this is discussing the same topic as your old thread. We ask that members please stick to one thread per topic, even if you've made tweaks.