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

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Posted (edited)
20 minutes ago, studiot said:

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


{f(x):f(x)=1,x0,f(x)=0,x=0;xR}

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

 

 

 

that functional expression is equivalent expression of 

f(x)= | sgn(x) | ,x is the element of R.

I understand.

Quote

 Note that we can handle infinity and use infinity in Mathematics, but infinity is not 'almost infinity' it is infinity.  

:) :) :) 

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Quote

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.

I was more trying to judge the claim that swansont had given. What does "physical" mean ? (for an expression) (what is the criterion?)

Edited by ahmet

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2 hours ago, ahmet said:

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

I thought you were referring to multiple reflections.(you said flat mirrors)

But for lenses and concave mirrors, you never physically have an object or image at an infinite distance. That’s a mathematical issue.

 

Quote

I was more trying to judge the claim that swansont had given. What does "physical" mean ? (for an expression) (what is the criterion?)

There is no physical realization. Nothing that can actually exist in the real world.

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2 minutes ago, ahmet said:

I understand.

Yes, that's a shorter way to put it.

5 minutes ago, ahmet said:

I was more trying to judge the claim that swansont had given. What does "physical" mean ? (for an expression) (what is the criterion?)

Physical can mean either that in some experiment we extrapolate along an asymptote as joigus has offered.
My example from analytical chemistry of infinite dilution would be where you might do this, but there are many pratical situations where this might happen eg measuring the charge on a capacitor.
My example from Thermodynamics is of the type mentioned by swansont where a heat sink or source is such that its temperature is not altered by the addition or extraction of some particular quantity of heat. That is how Carnot cycles are analysed.

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Posted (edited)
23 minutes ago, swansont said:

I thought you were referring to multiple reflections.(you said flat mirrors)

But for lenses and concave mirrors, you never physically have an object or image at an infinite distance. That’s a mathematical issue.

 

There is no physical realization. Nothing that can actually exist in the real world.

if I understand you correctly , you...

presumably want something that allow us to make any physical experiment or have a consciousness by our 5 sense organs. 

if so, or something like this. Then yes. assume please there are two flat mirrors each are in the opposing each other. (but think two cases) (to me,you could find the similar contexts in either examples  among the discussion) 

1) the mirrors are two circle mirrors and here our radius is infinity. 

2) in this second case. assume please the the mirror are in rectangular shape. 

then two subcases exists.

2a) assume please the angle between these two flat mirror is 180 degree. 

2b) assume please you are playing/changing with angle (only between -10,+10)

what will you see?

this is the tunnel and the frame. the inside of that rectangular frame is infinitive , but the count of frames are also infinitive.

you see the frames each.then it has been experimentally measured and mathematically can be formulated. 

for mathematical appearance and formulization

give a variation to the distance between each consecutive frame. (you see them)

and our function is dst(x) = {x, x= distance between each consecutive two frames}

then Kpl(t)= {t,t= count of domain set of dst(x) function}

.....

 

 

 

 

Edited by ahmet

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20 minutes ago, ahmet said:

if I understand you correctly , you...

presumably want something that allow us to make any physical experiment or have a consciousness by our 5 sense organs. 

if so, or something like this. Then yes. assume please there are two flat mirrors each are in the opposing each other. (but think two cases) (to me,you could find the similar contexts in either examples  among the discussion) 

1) the mirrors are two circle mirrors and here our radius is infinity. 

2) in this second case. assume please the the mirror are in rectangular shape. 

then two subcases exists.

2a) assume please the angle between these two flat mirror is 180 degree. 

2b) assume please you are playing/changing with angle (only between -10,+10)

what will you see?

this is the tunnel and the frame. the inside of that rectangular frame is infinitive , but the count of frames are also infinitive.

you see the frames each.then it has been experimentally measured and mathematically can be formulated. 

for mathematical appearance and formulization

give a variation to the distance between each consecutive frame. (you see them)

and our function is dst(x) = {x, x= distance between each consecutive two frames}

then Kpl(t)= {t,t= count of domain set of dst(x) function}

.....

 

 

 

 

 

Let us say that this was a good try at an idealisation,

BUT

Just as with a discharging capacitor that in theory takes forever to discharge fully, your photon would take forever to bounce back and fore whetween the mirrors a countable infinity of times.

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and, as I said earlier, there is absorption (and possibly transmission), so you eventually run out of photons. 

In a good cavity, the lifetime of a photon is still much, much less than a second.

good cavity, 2 ns lifetime:

 oe-15-25-17206.pdf?da=1&id=148384&seq=0& 

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8 minutes ago, ahmet said:

one of my hodja was using something like this:

Now I understand what you mean with one of your "hodja." I thought you were talking about an invisible friend. :) 

"Continuous everywhere" is another expression intended to be intuitive rather than rigorous, but is more traditional. It's to do with measure (cardinality, number of things,) rather than size.

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Posted (edited)
4 hours ago, joigus said:

Now I understand what you mean with one of your "hodja." I thought you were talking about an invisible friend. :) 

"Continuous everywhere" is another expression intended to be intuitive rather than rigorous, but is more traditional. It's to do with measure (cardinality, number of things,) rather than size.

as it said, my hodja means someone who was "hodja" from my BSc.(not my friend exactly)

however, I am about to accept/assume that do not understand / differentiate some terminoogy in matematics. 

because I did not use "continuous everywhere" ,where is that? ,I used "continuous almost everywhere". 

in anyway, I might consider studying a bit physics more. 

because I have not understood what swansont meant very well and / or what the criteria were ,for a description to be accepted as "physical" 

...

 

Edited by ahmet

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Posted (edited)
27 minutes ago, ahmet said:

as it said, my hodja means someone who was "hodja" from my BSc.(not my friend exactly)

however, I am about to accept/assume that do not understand / differentiate some terminoogy in matematics. 

because I did not use "continuous everywhere" ,where is that? ,I used "continuous almost everywhere". 

in anyway, I might consider studying a bit physics more. 

because I have not understood what swansont meant very well and / or what the criteria were ,for a description to be accepted as "physical" 

...

 

English has a technical word for objects in the general sense that is nouns.

But English is blessed because it distinguishes between certain types of noun.
In particular it distinguishes 'abstract' nouns and 'concrete' nouns.

Abstract nouns are objects that only exist in the mind. They are concepts.
Concrete nouns exist in physical reality, they have physical substance. You can pick one up and weigh it, poke it and so on.

So a cow is a concrete noun and a unicorn is an abstract noun.
So swansont's physical is our attempt to create a physical version of a theoretical object which means 'as close as we can get'.

I have tried to draw this distinction in my examples in the previous posts.

 

Does this help?

Secondly, by saying you understood my explanation of 'almost' I hope you understood that this means the process 'as close as we can get' in the physical world.

I hope you understood the distinction between the single discontinuous point and the infinity of continuous ones.
This distinction becomes very important in the branch of mathematics known as Analysis because there are types of discontinuity.
One of these is known as a 'removable discontinuity' which property greatly assists analysis.

Edited by studiot

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29 minutes ago, studiot said:

 

Secondly, by saying you understood my explanation of 'almost' I hope you understood that this means the process 'as close as we can get' in the physical world.

I hope you understood the distinction between the single discontinuous point and the infinity of continuous ones.
This distinction becomes very important in the branch of mathematics known as Analysis because there are types of discontinuity.
One of these is known as a 'removable discontinuity' which property greatly assists analysis.

these are already known.(because you are mentioning very basic subsubjecs

but I am not sure that that man knows all these instructions (in maths)

meanwhile,I think I can add some more (like ,separable spaces, first class spaces and 2nd class spaces, Lebesgue integral space)

....

English has a technical word for objects in the general sense that is nouns.

But English is blessed because it distinguishes between certain types of noun.
In particular it distinguishes 'abstract' nouns and 'concrete' nouns.

Abstract nouns are objects that only exist in the mind. They are concepts.
Concrete nouns exist in physical reality, they have physical substance. You can pick one up and weigh it, poke it and so on.

So a cow is a concrete noun and a unicorn is an abstract noun.
So swansont's physical is our attempt to create a physical version of a theoretical object which means 'as close as we can get'.

I have tried to draw this distinction in my examples in the previous posts.

Dear studiot, 

I do not think that all of these explanations were scientific

(the criteria or a criterion) 

and I why not to wait swansont let us learn more from him?

but of course,I might need to study a bit physics.

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Posted (edited)
1 hour ago, ahmet said:

however, I am about to accept/assume that do not understand / differentiate some terminoogy in matematics. 

I just forgot to type "almost." It's not my intention to take this discussion even farther off-topic than you already have. The OP was not about continuity almost everywhere anyway. If you don't speak English and are using google translator, it's OK. You just say so or ask for help. The OP has nothing to do with the measure of a set, but with the size of a quantity.

You also mistype, right? For example, "terminoogy", "matematics", or my favourite:

29 minutes ago, ahmet said:

subsubjecs

What are those? :) 

If you've got time, take a look at this word in the Oxford dictionary: "disingenuous."

15 hours ago, ahmet said:

presumably want something that allow us to make any physical experiment or have a consciousness by our 5 sense organs. 

That's not even a sentence in English. Here's the proof (and mind you, the parser is only concerned with syntax, we could talk about meaning):

No complete linkages found.
++++Time                                          0.05 seconds (30.83 total)
Found 204 linkages (59 with no P.P. violations) at null count 4
  Linkage 1, cost vector = (UNUSED=4 DIS=0 AND=2 LEN=43)

                                                                +-------
                                                                +-------
    +---------Wi--------+----------------TOo---------------+    |    +--
    |          +----E---+---Os--+                          +--I-+    |  
    |          |        |       |                          |    |    |  
LEFT-WALL presumably want.v something [that] [allow] [us] to make.v any 


-----------------------MVp-----------------------------+               
----Os-----------+                                     +---------Jp----
-------Ds--------+                                     |     +-----Dmcn
     +-----A-----+                                     |  +DD+    +---A
     |           |                                     |  |  |    |    
physical.a experiment.n or have.v [a] consciousness.n by our 5 sense.n 


----+
----+
N---+
    |
organs.n 


    +---------Wi--------+----------------TOo---------------+            
    |          +----E---+---Os--+                          +------------
    |          |        |       |                          |            
LEFT-WALL presumably want.v something [that] [allow] [us] to make.v any 


                                                       +---------Jp----
                              +-----------MVp----------+     +-----Dmcn
--------If--------------------+------Os------+         |  +DD+    +---A
                              |              |         |  |  |    |    
physical.a experiment.n or have.v [a] consciousness.n by our 5 sense.n 


----+
----+
N---+
    |
organs.n 

Constituent tree:

(S (VP (ADVP presumably)
       want
       (NP something)
       that allow us
       (S (VP to
              (VP make
                  (NP (NP any physical experiment)
                      or have a
                      (NP consciousness))
                  (PP by
                      (NP (QP our 5)
                          sense organs)))))))
Edited by joigus
unintentional rendering of characters as an icon

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14 hours ago, swansont said:

and, as I said earlier, there is absorption (and possibly transmission), so you eventually run out of photons. 

In a good cavity, the lifetime of a photon is still much, much less than a second.

good cavity, 2 ns lifetime:

 

That's not a good cavity.
This is an article about deliberately absorptive cavities with time constants over a thousand times longer.
https://en.wikipedia.org/wiki/Cavity_ring-down_spectroscopy


Though it's still well below 1 second.

(As an aside, I suspect the LIGO cavities would have a ring down time constant of over a second; that's a really good cavity, but not terribly practical.)

More importantly, back at the topic.

 

Isn't "almost infinite" the reciprocal of "practically nothing"?

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12 minutes ago, joigus said:

I just forgot to type "almost." It's not my intention to take this discussion even farther off-topic than you already have. The OP was not about continuity almost everywhere anyway. If you don't speak English and are using google translator, it's OK. You just say so or ask for help. The OP has nothing to do with the measure of a set, but with the size of a quantity.

You also mistype, right? For example, "terminoogy", "matematics", or my favourite:

What are those? :) 

If you've got time, take a look at this word in the Oxford dictionary: "disingenuous."

That's not even a sentence in English. Here's the proof (and mind you, the parser is only concerned with syntax, we could talk about meaning😞


No complete linkages found.
++++Time                                          0.05 seconds (30.83 total)
Found 204 linkages (59 with no P.P. violations) at null count 4
  Linkage 1, cost vector = (UNUSED=4 DIS=0 AND=2 LEN=43)

                                                                +-------
                                                                +-------
    +---------Wi--------+----------------TOo---------------+    |    +--
    |          +----E---+---Os--+                          +--I-+    |  
    |          |        |       |                          |    |    |  
LEFT-WALL presumably want.v something [that] [allow] [us] to make.v any 


-----------------------MVp-----------------------------+               
----Os-----------+                                     +---------Jp----
-------Ds--------+                                     |     +-----Dmcn
     +-----A-----+                                     |  +DD+    +---A
     |           |                                     |  |  |    |    
physical.a experiment.n or have.v [a] consciousness.n by our 5 sense.n 


----+
----+
N---+
    |
organs.n 


    +---------Wi--------+----------------TOo---------------+            
    |          +----E---+---Os--+                          +------------
    |          |        |       |                          |            
LEFT-WALL presumably want.v something [that] [allow] [us] to make.v any 


                                                       +---------Jp----
                              +-----------MVp----------+     +-----Dmcn
--------If--------------------+------Os------+         |  +DD+    +---A
                              |              |         |  |  |    |    
physical.a experiment.n or have.v [a] consciousness.n by our 5 sense.n 


----+
----+
N---+
    |
organs.n 

Constituent tree:

(S (VP (ADVP presumably)
       want
       (NP something)
       that allow us
       (S (VP to
              (VP make
                  (NP (NP any physical experiment)
                      or have a
                      (NP consciousness))
                  (PP by
                      (NP (QP our 5)
                          sense organs)))))))

and you give yourself a reasonable explanation  but do not give the same opportunity to other people. What a selfish manner :) :) 

anyway, I am very busy with more important things to do,and do not consider to reply further.

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