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King E

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

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Posted (edited)

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?

 

Edited by King E

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Where in the video, or alternatively, provide a transcript.

 

From the first ten seconds, though, I was not impressed, so it may be that there’s just no real credibility here.

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Just now, swansont said:

Where in the video, or alternatively, provide a transcript.

 

From the first ten seconds, though, I was not impressed, so it may be that there’s just no real credibility here.

1:23

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1 minute ago, King E said:

1:23

Yes, the use of the phrase there is bogus. It’s not a very good video, in many ways.

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1 minute ago, swansont said:

Yes, the use of the phrase there is bogus. It’s not a very good video, in many ways.

So can I say ''infinite pieces'' of vertical lines instead of ''almost infinite pieces''?

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1 hour ago, King E said:

So can I say ''infinite pieces'' of vertical lines instead of ''almost infinite pieces''?

The video depicts a finite number of elements of a finite height. It says that a dimension is small, “almost zero small” which is wrong

I don’t see why “infinte” should be mentioned at all.

Don’t subject yourself to this video any further. Someone else on youtube must have done a better job.

 

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Just now, swansont said:

The video depicts a finite number of elements of a finite height. It says that a dimension is small, “almost zero small” which is wrong

I don’t see why “infinte” should be mentioned at all.

Don’t subject yourself to this video any further. Someone else on youtube must have done a better job.

 

Thanks for guidance. 🙂

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1 hour ago, swansont said:

Yes, the use of the phrase there is bogus. It’s not a very good video, in many ways.

Just forget this video, as swansont says it is not good.

In fact it is worse than not good because it actually states some incorrect ideas further on.

In particular the idea that to make a 4D object we pack 3D objects 'inside it' .

Did you like Gabriel's horn?

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5 minutes ago, swansont said:

The video depicts a finite number of elements of a finite height. It says that a dimension is small, “almost zero small” which is wrong

I don’t see why “infinte” should be mentioned at all.

Don’t subject yourself to this video any further. Someone else on youtube must have done a better job.

 

Can you suggest a video or an article on dimensions(geometry) ?

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3Blue1Brown is a very high quality channel for maths, IMO. And Mathologer. Mathologer is especially rigorous while intuitive at the same time. I don't remember if they have anything on infinitesimals or geometry, but I'm sure they have.

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More specific to the OP

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

Limits approach a value, but never actually get there.
And are a very useful mathematical tool.

 

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18 hours ago, King E said:

As someone who hasn't studied very much math, "almost infinite" sounds like nonsense.

@MigL is right. More to the point. Almost infinite is nonsense. If someone gives you an "almost infinite" number, multiply it by 10^10^10...^10 and it's "almost nothing" no matter how big it looked.

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Posted (edited)

 

On 6/10/2020 at 6:01 PM, King E said:

So can I say ''infinite pieces'' of vertical lines instead of ''almost infinite pieces''?

to me,,"almost infinite" definitely does not make sense at this stage. 

but if we  were implying some contexts,for instance, in real analysis (some relevant subtitles would be : lebesgue integral, limits  specifically in this context, lebsgue space,etc.)then I m not sure.

Edited by ahmet

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Posted (edited)
Quote

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

 

In mathematics the problem is the 'almost'. So no it makes no sense.

In Physical Science then yes phrase may have value, for instance an 'almost infinite thermal reservoir' in Thermodynamics or 'almost infinite dilution' in Chemistry.

In each physical case the phrase measn that the quantity concerned is so large compared to the change considered that the quantity is constant or unaffected by the change.

This is just making use of one mathematical property of infinity that infinity plus or minus x is still infinity.

Edited by studiot

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Or, to put studiot's physical science example another way, it's saying that the system is large enough that the small changes are outside of any experimental determination, while acknowledging that using "infinite" is unphysical.

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1 hour ago, swansont said:

 while acknowledging that using "infinite" is unphysical.

I think it is physical,too.

because I think I can examplify it..

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Just now, ahmet said:

I think it is physical,too.

because I think I can examplify it..

Don’t leave us in suspense 

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1 minute ago, swansont said:

Don’t leave us in suspense 

well, 

assume please you use two flat mirror one is just at the opposing side another.

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1 minute ago, ahmet said:

well, 

assume please you use two flat mirror one is just at the opposing side another.

Two mirrors is not infinite. Please don’t make me drag this out of you. Post your example, or step off

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Just now, swansont said:

Two mirrors is not infinite. Please don’t make me drag this out of you. Post your example, or step off

I do not imply the mirror ,but ..

the appearances you will obtain ,will have at inifitive count.

 

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1 hour ago, ahmet said:

I do not imply the mirror ,but ..

the appearances you will obtain ,will have at inifitive count.

 

No, you will eventually run out of photons as there is absorption 

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27 minutes ago, swansont said:

No, you will eventually run out of photons as there is absorption 

I am not sure what you meant here. 

but this  might prove that it was physical (or in other words,it might convince you). (I could not be sure whether it complies this forum's rules ,therefore I am uploading the picture instead)

 

DSC_0051.jpg

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The only mathematical sense I can think of in which something being "almost infinite" (although that's not the proper way to say it) is asymptotics. This, in mathematics, is what most closely connects with what @studiot is saying:

6 hours ago, studiot said:

In mathematics the problem is the 'almost'. So no it makes no sense.

In Physical Science then yes phrase may have value, [...]

+1. Though you'd be well advised not to use the words "almost zero" or "almost infinite" in those cases. Take, for example, the number 10120 compared with 1. The wrong way to say it is "10120 is almost infinite." A better way to say it is, 

\[10^{120}+1\sim10^{120}\]

Although the proper context is with functions. Example:

\[f\left(x\right)\sim e^{x}\]

\[g\left(x\right)\sim x\]

Which means that f is ginormously bigger than g when x is big.

The "almost" operator (\sim in LateX) defines an equivalence class (same limiting behaviour.) And you should never use it in combination with 0 or infinity.

I hope that helps.

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Posted (edited)

mmm,maybe I might change my idea. :) :) 

because I remember at one of my BSc class that one of my hodja was using something like this:

"continuous Almos at everywhere"

but again I am sure on one thing.

to make it in the conformity of mathematical sense, you need to formulate it.

and I do not remember the formula of that things he said (given above) 

8 hours ago, ahmet said:

 

to me,,"almost infinite" definitely does not make sense at this stage. 

but if we  were implying some contexts,for instance, in real analysis (some relevant subtitles would be : lebesgue integral, limits  specifically in this context, lebsgue space,etc.)then I m not sure.

mm yes presumably I am correct in this expression.

because when I asked to google what "continuous almost everywhere " means ,it returned me this quotation given below

Quote

A function f:X→Y is continuous almost everywhere if it is only discontinuous on a set of measure 0. ... There is an important distinction to make here: a function is continuous almost everywhere if it is continuous on a "large" subset. But it must be continuous on that subset.

this explanation includes one important keyword "measure" thus it is presumably relevant to real analsysi ("measure theory")

 

Edited by ahmet
I could not refine it very well,sorry

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1 hour ago, ahmet said:

because when I asked to google what "continuous almost everywhere " means ,it returned me this quotation given below

An example of a function that is 'continuous almost everywhere would be


[math]\left\{ {f\left( x \right):f\left( x \right) = 1,x \ne 0,f\left( x \right) = 0,x = 0;x \in R} \right\}[/math]

Here the function is continuous for an infinity of points but discontinuous for one single point at the origin.

 

Note that we can handle infinity and use infinity in Mathematics, but infinity is not 'almost infinity' it is infinity.
For example the 'point or line at infinity' in projective geometry.
This is example is different from your optics one since your table says both that the image does not exist and the image is at infinity.
A better optical example would be a source (object) at infinity, which has meaning.

 

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