Can the definition of infinity disprove an infinite past?

[untermensche]

What is a countable infinity?

And perhaps a stupid question.

What is the definition of infinity?

I have seen none in this thread about the logical consequences that flow from the definition of infinity.

What is infinity?

Hard to move one step until the main term of the discussion is vigorously defined.

Does the concept of infinite time include an amount of time that has completed?

Not a stupid question at all.

There's a tutorial on types of infinity here..... I think your "amount of time that has completed" may be a countable infinity, but other parts of the discussion may be uncountable.

I appreciate at least some effort, but:

Because we could list all these integers between two randomly chosen integers we say that the integers are countably infinite. Again, there is no real reason to actually do this, it is simply something that can be done if we should chose to do so.

Labeling things "countable" for no reason doesn't seem to me to be clarifying the concept.

Are the positive integers countable?

Could they be counted?

How could they be counted?

No matter how many were named there would still be infinite more not named. This will never change. It is impossible to approach the completion of counting the positive integers. There is no end to it.

So is it possible for an infinite amount of time to end?

Like all the time in the past ends continually at the ever changing present?

 

[steve_bank]

There's been a lot of references to infinity in this thread, but what kind of infinity? Countable or uncountable?

As an old maths tutor I used to know said "Infinity is not a number, and mostly doesn't behave like one". This being a maths forum, we ought to be rigorous.

What is a countable infinity?

And perhaps a stupid question.

What is the definition of infinity?

I have seen none in this thread about the logical consequences that flow from the definition of infinity.

What is infinity?

Hard to move one step until the main term of the discussion is vigorously defined.

Does the concept of infinite time include an amount of time that has completed?

What is the definition of many? When ancient Zog ciunted mastedons and used up his fingers and toes he might have opened his arms wide and grunted a sound meaning many, uncountable.

More precisely or rigorously, the limit as x ->0 1/x is infinity. Here infinity means an unreacable or uncountable number of iterations. An asymptote. For every x there is an x+1 that can be calculated. There is no mathematical algorith or amalog or digital circuit that can divide by exactly zero.

Or a series from high school algebra. 1, 2, 3...infinity. Three terms to identify the sequence. There is no possible end to the sequence. Other than running out of paper or memory storage.

In a simple algorithm in words how would you describe the growth of i?
i=0
start
print i
i = i + 1
goto start

 

[steve_bank]

In set theory there are icountably infinite sets in that infinities can be added, but I belive there is no possible numerical countable infinity.

The set of all real numbers between 2 and 3 is bounded but infinite. The number of indexes into the set is infinite.

In the set of integers from 1 to 10 the set is bounded and finite. A finite number of indexes into the set.

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

The notion of cardinality, as now understood, was formulated by Georg Cantor, the originator of set theory, in 1874–1884. Cardinality can be used to compare an aspect of finite sets; e.g. the sets {1,2,3} and {4,5,6} are not equal, but have the same cardinality, namely three (this is established by the existence of a bijection, i.e. a one-to-one correspondence, between the two sets; e.g. {1→4, 2→5, 3→6}).

Cantor applied his concept of bijection to infinite sets;[1] e.g. the set of natural numbers N = {0, 1, 2, 3, ...}. Thus, all sets having a bijection with N he called denumerable (countably infinite) sets and they all have the same cardinal number. This cardinal number is called {\displaystyle \aleph _{0}} \aleph _{0}, aleph-null. He called the cardinal numbers of these infinite sets transfinite cardinal numbers.

 

[Juma]

More precisely or rigorously, the limit as x ->0 1/x is infinity. Here infinity means an unreacable or uncountable number of iterations. An asymptote. For every x there is an x+1 that can be calculated. There is no mathematical algorith or amalog or digital circuit that can divide by exactly zero.

Limits are not defined by iterations. It is defined by the single statement you wrote: that the value is bigger than an bigger than any value.

 

[Bomb#20]

I appreciate at least some effort, but:

Because we could list all these integers between two randomly chosen integers we say that the integers are countably infinite. Again, there is no real reason to actually do this, it is simply something that can be done if we should chose to do so.

Labeling things "countable" for no reason doesn't seem to me to be clarifying the concept.

Mathematicians, like dentists and every other technical profession, have their own peculiar terminology for technical concepts. They of course do not call infinities "countable" for no reason -- you might as well accuse your dentist of calling your cavity a "caries" for no reason -- but the reason mathematicians call some infinities "countable" wouldn't impress you. You wouldn't think it's a good reason, because you have different priorities from mathematicians. And that's fine -- there's no reason what's important to them should be important to you -- but that cuts both ways. So why make an issue of it? For all practical purposes they might as well be calling those particular infinities "crispy". It's just technical jargon. When they say "countable", all they mean is "as many as the integers". They say "countable" to make a distinction that's important to them -- some infinities are as numerous as the integers and other infinities they call "uncountable" are more numerous than the integers -- but if the distinction between the two categories of infinity isn't important to you then feel free to skip over all the "countable"s when you hear people talking about infinity. But telling people they're wrong because the infinities they call "countable" can't be counted is just lame -- you and they are simply using the word "countable" in two different senses. That's language for you -- there are more concepts than words, so people recycle words. There's no point getting worked up about it. Just imagine they're talking about crispy infinities vs. mushy infinities, and move on.

 

[untermensche]

There's been a lot of references to infinity in this thread, but what kind of infinity? Countable or uncountable?

As an old maths tutor I used to know said "Infinity is not a number, and mostly doesn't behave like one". This being a maths forum, we ought to be rigorous.

What is a countable infinity?

And perhaps a stupid question.

What is the definition of infinity?

I have seen none in this thread about the logical consequences that flow from the definition of infinity.

What is infinity?

Hard to move one step until the main term of the discussion is vigorously defined.

Does the concept of infinite time include an amount of time that has completed?

What is the definition of many?

If you have any amount of things that take up a finite space the amount of those things are also finite.

The number of grains of sand on the earth at any given moment are finite.

More precisely or rigorously, the limit as x ->0 1/x is infinity.

This is an infinite mathematical operation. Not a definition.

What is the definition of infinity?

In words.

Is it something that cannot be defined using only words?

How exactly are we supposed to say anything about infinity unless it is vigorously defined?

Can it be defined as opposed to just depicted with symbols?

 

[untermensche]

I appreciate at least some effort, but:

Because we could list all these integers between two randomly chosen integers we say that the integers are countably infinite. Again, there is no real reason to actually do this, it is simply something that can be done if we should chose to do so.

Labeling things "countable" for no reason doesn't seem to me to be clarifying the concept.

Mathematicians, like dentists and every other technical profession, have their own peculiar terminology for technical concepts. They of course do not call infinities "countable" for no reason -- you might as well accuse your dentist of calling your cavity a "caries" for no reason -- but the reason mathematicians call some infinities "countable" wouldn't impress you. You wouldn't think it's a good reason, because you have different priorities from mathematicians. And that's fine -- there's no reason what's important to them should be important to you -- but that cuts both ways. So why make an issue of it? For all practical purposes they might as well be calling those particular infinities "crispy". It's just technical jargon. When they say "countable", all they mean is "as many as the integers". They say "countable" to make a distinction that's important to them -- some infinities are as numerous as the integers and other infinities they call "uncountable" are more numerous than the integers -- but if the distinction between the two categories of infinity isn't important to you then feel free to skip over all the "countable"s when you hear people talking about infinity. But telling people they're wrong because the infinities they call "countable" can't be counted is just lame -- you and they are simply using the word "countable" in two different senses. That's language for you -- there are more concepts than words, so people recycle words. There's no point getting worked up about it. Just imagine they're talking about crispy infinities vs. mushy infinities, and move on.

I make a point of it to get these kinds of clarifications.

It is just a label.

Not really saying any infinity is countable.

Or if we say infinite time.

It could never be an amount of time that is passable. It could never pass.

Yet the entirety of the time in the past has passed at every present moment.

 

[steve_bank]

More precisely or rigorously, the limit as x ->0 1/x is infinity. Here infinity means an unreacable or uncountable number of iterations. An asymptote. For every x there is an x+1 that can be calculated. There is no mathematical algorith or amalog or digital circuit that can divide by exactly zero.

Limits are not defined by iterations. It is defined by the single statement you wrote: that the value is bigger than an bigger than any value.

They are defined by iteration, that is the process. Same with a derivative.

1/[ 2 + (1/x)] goes to 1/2 in the process as x goes to but never reaches zero. Limits and asymptotes are a sequential process.

 

[steve_bank]

What is the definition of many?

If you have any amount of things that take up a finite space the amount of those things are also finite.

The number of grains of sand on the earth at any given moment are finite.

More precisely or rigorously, the limit as x ->0 1/x is infinity.

This is an infinite mathematical operation. Not a definition.

What is the definition of infinity?

In words.

Is it something that cannot be defined using only words?

How exactly are we supposed to say anything about infinity unless it is vigorously defined?

Can it be defined as opposed to just depicted with symbols?

I point to an object and it is a rock, it is a definition. Infinity is mathematically real examples which are pointed to and labeled.

I gave two simple examples. Take pen and paper and start calculating 1/x at 100,200,300... Plot the results on graph paper. Infinity is not an object or number, in this case infinity is growth without bound. I do not see how it can be understood without applying it. Trying to intectualize it gets nowhere.

 

[Juma]

More precisely or rigorously, the limit as x ->0 1/x is infinity. Here infinity means an unreacable or uncountable number of iterations. An asymptote. For every x there is an x+1 that can be calculated. There is no mathematical algorith or amalog or digital circuit that can divide by exactly zero.

Limits are not defined by iterations. It is defined by the single statement you wrote: that the value is bigger than an bigger than any value.

They are defined by iteration, that is the process. Same with a derivative.

1/[ 2 + (1/x)] goes to 1/2 in the process as x goes to but never reaches zero. Limits and asymptotes are a sequential process.

No it is not. It isnt a process at all. You may use iterations to make a approximative calculation but that is not the same thing as the limit itself.

 

[untermensche]

I point to an object and it is a rock, it is a definition.

Really?

What kind of rock is it?

Infinity is mathematically real examples which are pointed to and labeled.

You gave infinite operations.

Not infinity.

What is infinity?

 

[bilby]

They are defined by iteration, that is the process. Same with a derivative.

1/[ 2 + (1/x)] goes to 1/2 in the process as x goes to but never reaches zero. Limits and asymptotes are a sequential process.

No it is not. It isnt a process at all. You may use iterations to make a approximative calculation but that is not the same thing as the limit itself.

He's an engineer. They think processes are so important that they actually are the facts that they represent. He probably thinks that, as one can count to ten on ones fingers, numbers greater than about eighty billion are impossible, because there are not enough fingers in the world.

 

[steve_bank]

I point to an object and it is a rock, it is a definition.

Really?

What kind of rock is it?

Infinity is mathematically real examples which are pointed to and labeled.

You gave infinite operations.

Not infinity.

What is infinity?

I will give it one more try. Infinity as a mathematical label for an observed mathemetacal result. There is no other, anything else is philosopy. There is no meaning to infinity any more than wwhat 1 + 1 = 2 means. You and others are looking for something deeper that is not there.

Sealing with infibities is first learned in algebra and calculus. In control systems innities are mathematcasly called a singularity, and when a the denominator of a system equation tries to go to zero. Mathematicaly the eigenvalues and eigenvectors of the system equation. Infinity is the result of a mathemeatical operation.

 

[steve_bank]

They are defined by iteration, that is the process. Same with a derivative.

1/[ 2 + (1/x)] goes to 1/2 in the process as x goes to but never reaches zero. Limits and asymptotes are a sequential process.

No it is not. It isnt a process at all. You may use iterations to make a approximative calculation but that is not the same thing as the limit itself.

He's an engineer. They think processes are so important that they actually are the facts that they represent. He probably thinks that, as one can count to ten on ones fingers, numbers greater than about eighty billion are impossible, because there are not enough fingers in the world.

I am searching for the right words. I am sorry if I...intimidate you. With someone's help I debunked your assertion that QFT was some redefinition of energy, take a look at the QFT thread. There were other assertions of yours.

I am not putting you are ignore, but you are going to have to do a lot more than try to insult enginering to get me going. I worked in dog eat dog competitive environments where being right mattered and superflous bloviting was a career killer.

Applying control systems requires complex variables, state variables, and linear algebra, plus a theoretical mathemetical framework.

The general priciples and math are the same across physics, electrical, and mechanical engineering. Resonance for one exists electricaly, mechanically, and atomically. The names are different in different areas. A wave packet in QM has its correlary for a wave pulse in a trasmission line.EM .

When a took a modern physics night class in the early 90s it was anticlimatic. Fourier Transforms, probability distributions, linear algebra. Even techicians get basic QM applied to semiconductors, holes, electrons, donors, acceptors, doping. Most circuit designers understand bipolar and metalic oxide trasisistors down to the QM level. We need it to know which model to use for simulation.

Technician level
https://en.wikipedia.org/wiki/Bipolar_junction_transistor

Intermediate tecnician level level
http://people.seas.harvard.edu/~jones/es154/lectures/lecture_3/bjt_models/ebers_moll/ebers_moll.html


I could reccomend Streetman's Solid State Electronics, or Analysis and Design of Analog Integrated Circuits by Gray both undergard texts, but it requires calculus and physics. Both were on my work bookshelf. Streetman is a good read on aplied QM if you have the foundation.


As to your assertion engineering is simple approximations caompared to science, feel free to demonstrate. For once put your money where your mouth is. Put up or shut up, so to speak.

 

[steve_bank]

They are defined by iteration, that is the process. Same with a derivative.

1/[ 2 + (1/x)] goes to 1/2 in the process as x goes to but never reaches zero. Limits and asymptotes are a sequential process.

No it is not. It isnt a process at all. You may use iterations to make a approximative calculation but that is not the same thing as the limit itself.

You are conflating a sequential process with approximate numerical solutions. The general term is a 'non linear solver'. In physics and engineering you often end up with a set of nonlinear inegro differential equations. Non linear means they can not be solved by linear algebra. You can call rightly approximations, in practice systems of equations can be solved to any neccesary number of decimal places.

In principle doing a chain of equations by a slide rule, hand, or with a calculatur becomes an approximation based on the amount of storage for a digit. All compute numerical operations become approximations based on finite word length to represent numbers and the least significant bit of the digital word for a number..

A series is a sequential process. 1+1,1+2,1+3...infinity. Evaluating 1/x sequentially is a process. How do you find the two sided limit mathematically and at what pont do you say zero or infinity. 1,2,3 asymptoticaly goes to 0. 1,0.9.0.8... goes to imfinity. How do you prove it.

All limit situations in engineering functions are not so simple.

 

[untermensche]

Really?

What kind of rock is it?



You gave infinite operations.

Not infinity.

What is infinity?

I will give it one more try. Infinity as a mathematical label for an observed mathemetacal result.

The only thing that is observed is an infinite operation.

Infinity is not observed.

The infinity is an imagined result of running the operation.

But the operation will never finish.

The infinity will never be observed.

So again, what is the definition of infinity?

 

[bilby]

He's an engineer. They think processes are so important that they actually are the facts that they represent. He probably thinks that, as one can count to ten on ones fingers, numbers greater than about eighty billion are impossible, because there are not enough fingers in the world.

I am searching for the right words. I am sorry if I...intimidate you.

With someone's help I debunked your assertion that QFT was some redefinition of energy, take a look at the QFT thread. There were other assertions of yours.

I, like anyone else, have made a number of assertions. "that QFT was some redefinition of energy" has never been one of them, so it's impossible that you debunked it

I do recall your insane claim that it was necessary to have an energy source in order to cool an object in space; You got in a huge snit when I pointed out that your claim was crazy, and then I see you started a whole new thread to discuss the question, in which you came to realize that I was right.

I don't find your constant bald assertions of the bleeding bloody obvious, nor the fact that despite being sophomoric, they are often fundamentally wrong 'intimidating'; I find it bloody irritating, as it tends to derail promising discussions from which I might learn something and divert them into tedious rehashing of things I already know.

I am not putting you are ignore, but you are going to have to do a lot more than try to insult enginering to get me going.

I don't care about getting you going; But if I did, this post of yours would strongly suggest that I had succeeded.

I just took you off ignore. But I am immediately regretting that decision.

I worked in dog eat dog competitive environments where being right mattered and superflous bloviting was a career killer.

I can see why you used the past tense there then.

Applying control systems requires complex variables, state variables, and linear algebra, plus a theoretical mathemetical framework.

The general priciples and math are the same across physics, electrical, and mechanical engineering. Resonance for one exists electricaly, mechanically, and atomically. The names are different in different areas. A wave packet in QM has its correlary for a wave pulse in a trasmission line.EM .

When a took a modern physics night class in the early 90s it was anticlimatic. Fourier Transforms, probability distributions, linear algebra. Even techicians get basic QM applied to semiconductors, holes, electrons, donors, acceptors, doping. Most circuit designers understand bipolar and metalic oxide trasisistors down to the QM level. We need it to know which model to use for simulation.

Technician level
https://en.wikipedia.org/wiki/Bipolar_junction_transistor

Intermediate tecnician level level
http://people.seas.harvard.edu/~jones/es154/lectures/lecture_3/bjt_models/ebers_moll/ebers_moll.html


I could reccomend Streetman's Solid State Electronics, or Analysis and Design of Analog Integrated Circuits by Gray both undergard texts, but it requires calculus and physics. Both were on my work bookshelf. Streetman is a good read on aplied QM if you have the foundation.


As to your assertion engineering is simple approximations caompared to science, feel free to demonstrate. For once put your money where your mouth is. Put up or shut up, so to speak.

It's not an assertion, it's an observation. Would you find it impressive if I made a couple of dozen declarative but contentless statements, that were either too obvious to be worthy of comment (eg "The general priciples and math are the same across physics, electrical, and mechanical engineering"), or just name-dropping of concepts that there is no evidence I understand at all (eg "Fourier Transforms, probability distributions, linear algebra")?

Engineering is by necessity approximate, as are most sciences. That's not an insult, unless you have an overdeveloped need to be 'right'. Biologists don't bother trying to use QM to describe elephants. If you walk around with a chip on your shoulder, don't be surprised when someone knocks it off.

You look to me like a stupid person's idea of what they think a clever person looks like. Or like an over-eager undergraduate who is convinced not only that he knows everything, but that it is important to impress everyone else with his knowledge. You are deeply conservative, and lack the imagination or the will to consider that your engineering rules of thumb might not be universal physical laws. It's all image, and no substance.

Back to 'ignore' with you.

 

[steve_bank]

Really?

What kind of rock is it?



You gave infinite operations.

Not infinity.

What is infinity?

I will give it one more try. Infinity as a mathematical label for an observed mathemetacal result.

The only thing that is observed is an infinite operation.

Infinity is not observed.

The infinity is an imagined result of running the operation.

But the operation will never finish.

The infinity will never be observed.

So again, what is the definition of infinity?

Yes, infinity is not observed. It is a label for a conclusion may be one way to look at it. Philosophical conundrums occur when you try to use an abstract infinite number line to address cosmology. A lot of interesting twists and turns worth thinking through, but no resolution.

I posted a link on infinity on the other thread. It has been discussed for thousands of years. I do not see there is a definition per se. We say that for a given math or physical process we say a result grows without bound, infinity.

In physical control systems when a parameter called a pole approaches zero a singularity starts to occur. Some parameter will try to grow without bound. In a speed control system if a particular pole goes towards zero speed may try to increase without bounds, but never gets to infinite speed. It is limited by available energy or mechanical failure.A black hole approaches a singularity but never gets there. As the black hole forms density increases increasing gravity, but the matter density can never be infinite. It would suck up all the energy in the universe.

The principle of infinity is not just an abstraction, it has uses in science and engineering.

The principle of infiniy plays out in real physical systems. It is not just mathematical.

 

[steve_bank]

My good friend bilby,

You seem o have glommed onto me as an antagonist. Neither here nor there for me. With me you have a series of unsupported assertions. For example on the energy thread you asserted that QFT somehow redefined energy in a way that made standard thermodynamics a trivial approximation, without chapter and verse. On the QFT thread someone familiar with QFT refuted what you said. That plus the link in OP which stated as with QM QFT lends itself to a lot of philosophical speculation and interpretation, which was my first read of your assertion. You said according to QFT energy was 'everywhere', to which I replied like the Star Wars Force?

Discussion with you goes nowhere, you make generalizations with no support.. You are not on my ignore but feel free to rant at your pleasure.

If this was a competitive professional environment I'd give someone attacking as you do a bit of rope and then at the right time cut his balls off publically. Been there done that.

 

[Juma]

My good friend bilby,

You seem o have glommed onto me as an antagonist. Neither here nor there for me. With me you have a series of unsupported assertions. For example on the energy thread you asserted that QFT somehow redefined energy in a way that made standard thermodynamics a trivial approximation, without chapter and verse. On the QFT thread someone familiar with QFT refuted what you said. That plus the link in OP which stated as with QM QFT lends itself to a lot of philosophical speculation and interpretation, which was my first read of your assertion. You said according to QFT energy was 'everywhere', to which I replied like the Star Wars Force?

Discussion with you goes nowhere, you make generalizations with no support.. You are not on my ignore but feel free to rant at your pleasure.

If this was a competitive professional environment I'd give someone attacking as you do a bit of rope and then at the right time cut his balls off publically. Been there done that.

Cut his balls? LOL. Lot of hot air coming from your direction. Calm down and acknowledge that you dont know everything.

Here is an article about an energy that is everywhere: https://en.m.wikipedia.org/wiki/Vacuum_energy