B Does it make sense to say that something is almost infinite?

[SSG-E]

TL;DR Summary

Does it make sense to say that something is almost infinite? If yes, then why?

I remember hearing someone say "almost infinite" in this video. As someone who hasn't studied very much math, "almost infinite" sounds like nonsense. Either something ends or it doesn't, there really isn't a spectrum of unending-ness. In this video he says that ''almost infinite'' pieces of verticle lines are placed along X length. Why not infinit?

 

[member 587159]

No I'm not aware of any sense in which 'almost infinite' makes formal sense. In practise, I guess it means "a very large number".

From a context of ordinal numbers, the first infinite ordinal $\omega$ has no predecessor, that is there is no ordinal $\eta$ such that $\omega = \eta +1$. One says that $\omega$ is a limit ordinal.

 

[SSG-E]

No I'm not aware of any sense in which 'almost infinite' makes sense.

From a context of ordinal numbers, the first infinite ordinal $\omega$ has no predecessor, that is there is no ordinal $\eta$ such that $\omega = \eta +1$. One says that $\omega$ is a limit ordinal.

Then is it correct to say infinite pieces instead of almost infinite pieces in that video?

 

[member 587159]

Then is it correct to say infinite pieces instead of almost infinite pieces in that video?

I did not say something like that. This video tries to intuitively explain what dimension is. You shouldn't be looking for rigorous explanations in videos like that, but just to get a 'feeling' for the subject.

Infinite dimensional just means NOT finite dimensional (in the context of vector spaces at least).

 

[SSG-E]

I did not say something like that. This video tries to intuitively explain what dimension is. You shouldn't be looking for rigorous explanations in videos like that, but just to get a 'feeling' for the subject.

Infinite dimensional just means NOT finite dimensional (in the context of vector spaces at least).

I don't get it

 

[jedishrfu]

Things are either finite or infinite. There is no formal definition for almost infinite. Informally as @Math_QED said it means a really large number likely a number you can't write down in a reasonable amount of time.

Some famous cases of numbers are:

• googol =
  
• centillion =
  
  or
  
  , depending on number naming system.
• millillion =
  
  or
  
  , depending on number naming system.
• micrillion =
  
  or
  
  , depending on number naming system.
• The largest known Smith number = (101031−1) × (104594 + 3×102297 + 1)1476 ×103913210.
• The largest known Mersenne prime =
  
  (as of December 21, 2018),
• googolplex =
  
  .
• Skewes' numbers: the first is approximately
  
  , the second
  
  ,
• googolplexian =
  
  .
• Graham's number, larger than what can be represented even using power towers (tetration). However, it can be represented using Knuth's up-arrow notation.
• Rayo's number is a large number named after Agustín Rayo which has been claimed to be the largest named number. It was originally defined in a "big number duel" at MIT on 26 January 2007.

https://en.wikipedia.org/wiki/Large_numbers

It's like games of chance where people like to say they almost won. They either won or they lost there is nothing in between. You either won the money or lost the money but almost won sounds better especially when talking to your spouse.

 

[jbriggs444]

One could come up with a topological notion of "almost infinite". Consider, for instance the real number line compactified into a circle by adjoining a point at +/- infinity. Impose a topology on this circle by considering that the distance (metric) between a point x and infinity is given by $\frac{1}{\text{max}(1,|x|)}$

[I suspect one might have to juice up this metric a bit to make sure it obeys the triangle inequality. The easy way is to use the induced metric from the circle. Now all you have to do is map real values plus infinity to a circle -- something like arc-tangent]

Now you have a notion of "almost infinite" -- 1,000,000 is only 1/1,000,000 away from infinity.

 

[Svein]

Consider, for instance the real number line compactified into a circle by adjoining a point at +/- infinity

Or even map all complex numbers onto a sphere (the Riemann sphere):