What are the implications of an infinite large universe?

[klutedavid]

Apart from not answering my question it's painfully obvious you don't even understand what a finite set is.

I do understand. How about a set of monkeys that ignore definitions.[/Quote]A finite set is simply a set with a finite number of elements.The elements don't even have to be numbers they can be objects such pelicans, apples or aardvarks.In case of real numbers it doesn't matter that each number is finite, it's a case of counting each number in the set which is impossible given there are an infinite number of real numbers for any given interval or subset.[/QUOTE]Please explain what an 'infinite number' is?

Are you referring to transfinite numbers?

If you count the elements in any set, the count is always an integer value.

If you had a set of real numbers and no matter how large that set, there is always an integer count for each element in that set. So if one was to consider an infinite set of real numbers, then the elements of that set. Would require an infinite integer count. That is impossible of course because integers are finite numbers.

An infinite set of anything is a paradox.

 

[SelfSim]

Are you referring to transfinite numbers?

You are still playing word games. Transfinites are still conceptually infinite.

If you count the elements in any set, the count is always an integer value.

If you had a set of real numbers and no matter how large that set, there is always an integer count for each element in that set. So if one was to consider an infinite set of real numbers, then the elements of that set. Would require an infinite integer count. That is impossible of course because integers are finite numbers.

Integers are discrete, equally spaced numbers on an infinitely long number line.

 

[klutedavid]

You are still playing word games. Transfinites are still conceptually infinite.

Integers are discrete, equally spaced numbers on an infinitely long number line.

A number line is populated by finite numbers, an infinite number line is not possible. Finite numbers can never become infinite numbers.

Once again, infinite means unbounded, limitless, certainly not discrete.

Your number line starts at zero in the positive direction. Zero marks the boundary for all positive numbers on that number line. Since one end of the number line is bounded, then the number line in the positive direction cannot be infinite. The definition of infinite is unbounded!

 

[SelfSim]

Interesting .. it seems we might be seeing a serious roadblock on the pathway of conceptual learning here(?)
Definitions are not absolutes .. especially in science. In math, mathematicians actually occasionally develop proofs for their conceptual postulates too, y'know(?)

 

[SelfSim]

Your number line starts at zero in the positive direction. Zero marks the boundary for all positive numbers on that number line. Since one end of the number line is bounded, then the number line in the positive direction cannot be infinite. The definition of infinite is unbounded!

The same number line goes infinite in the negative integer direction too.

 

[klutedavid]

The same number line goes infinite in the negative integer direction too.

Your dreaming.

 

[klutedavid]

Interesting .. it seems we might be seeing a serious roadblock on the pathway of conceptual learning here(?)
Definitions are not absolutes .. especially in science. In math, mathematicians actually occasionally develop proofs for their conceptual postulates too, y'know(?)

Without definitions, language and communication is impossible.

 

[SelfSim]

Your dreaming.

.. and you're just wrong:

 

[SelfSim]

Without definitions, language and communication is impossible.

Definitions are contextually dependent.
Your mind is locked into a singularly fixed context.

 

[Freth]

I haven't read the thread, I just skimmed over a few posts, but has anyone looked at the elephant in the room? If the universe is expanding, what is giving it space to expand? Infinite nothingness? And how is it that a universe exists in an infinite nothingness that seemingly has no purpose whatsoever but to exist for the expanding universe? Since we don't know what's beyond the universe, we can't know, but I think it should at least give pause to anyone thinking about an expanding universe, to consider the nothingness beyond, in which it resides.

 

[Ponderous Curmudgeon]

A number line is populated by finite numbers, an infinite number line is not possible. Finite numbers can never become infinite numbers.

Once again, infinite means unbounded, limitless, certainly not discrete.

Your number line starts at zero in the positive direction. Zero marks the boundary for all positive numbers on that number line. Since one end of the number line is bounded, then the number line in the positive direction cannot be infinite. The definition of infinite is unbounded!

How many integers are there? What is the last integer on a number line?

 

[renniks]

No, you simply said that time wouldn't exist for God. But you said that He's infinite. That's a contradiction. Infinite doesn't mean to exist outside of time. It means to exist for all time. So from there, where does the argument break down?

I see no contradiction. Infinite and eternal equals timeless.

 

[sjastro]

I do understand. How about a set of monkeys that ignore definitions. Please explain what an 'infinite number' is?

Are you referring to transfinite numbers?

If you count the elements in any set, the count is always an integer value.

If you had a set of real numbers and no matter how large that set, there is always an integer count for each element in that set. So if one was to consider an infinite set of real numbers, then the elements of that set. Would require an infinite integer count. That is impossible of course because integers are finite numbers.

An infinite set of anything is a paradox.

No you do not understand.
Your insistence real numbers and now integers being finite numbers, then one cannot have an infinite set of either is incoherent.
This is primary school stuff and doesn’t require a PhD to comprehend.

A count is simply a positive integer which can also form an infinite set {0,1,2,3,4……………..}
Since you think this is not possible as each individual number in the set is finite what is the last term in the set?
The answer is you don’t know which in itself provides the definition of an infinite set as the last term is undefined.

Computer programmers know all too well about infinite integer counts.
Here is a program which counts the number of elements in a finite set.

rem "number of elements in set is finite and equals p."
c=0
input "number of elements in set";p
[start] c=c+1
if p=c then print c:end
goto [start]

c=0 initializes the count; c=c+1 is the integer count and the number of elements p is inputted into the program.
This is a loop program where the number of loops performed is p.
When the integer count equals the number of elements in the set, the program prints the number of elements in the set and stops.

Here is a program which attempts to count the number of elements in an infinite set.

rem "number of elements in set is infinite since p is not defined."
c=0
[start] c=c+1
if p=c then print c:end
goto [start]

The program performs an integer count for each loop but since p is not defined for an infinite set, the program will not stop as it will never find p.
The result is an infinite integer count in the form of an infinite or endless loop.
According to your ‘logic’ an endless loop is impossible as the integer count can never become infinite.

 

[klutedavid]

How many integers are there? What is the last integer on a number line?

There will always be a finite number of integers, since integers are finite numbers by definition.

There is no last finite integer on a number line, there will always be another greater finite integer.

If your number line is a finite number line, then all values along that number line must be finite.

The finite never can become the infinite as that is illogical.

 

[klutedavid]

No you do not understand.
Your insistence real numbers and now integers being finite numbers, then one cannot have an infinite set of either is incoherent.
This is primary school stuff and doesn’t require a PhD to comprehend.

A count is simply a positive integer which can also form an infinite set {0,1,2,3,4……………..}
Since you think this is not possible as each individual number in the set is finite what is the last term in the set?
The answer is you don’t know which in itself provides the definition of an infinite set as the last term is undefined.

Computer programmers know all too well about infinite integer counts.
Here is a program which counts the number of elements in a finite set.

rem "number of elements in set is finite and equals p."
c=0
input "number of elements in set";p
[start] c=c+1
if p=c then print c:end
goto [start]

c=0 initializes the count; c=c+1 is the integer count and the number of elements p is inputted into the program.
This is a loop program where the number of loops performed is p.
When the integer count equals the number of elements in the set, the program prints the number of elements in the set and stops.

Here is a program which attempts to count the number of elements in an infinite set.

rem "number of elements in set is infinite since p is not defined."
c=0
[start] c=c+1
if p=c then print c:end
goto [start]

The program performs an integer count for each loop but since p is not defined for an infinite set, the program will not stop as it will never find p.
The result is an infinite integer count in the form of an infinite or endless loop.
According to your ‘logic’ an endless loop is impossible as the integer count can never become infinite.

Not my logic. Integers are finite numbers.

I would advise you to place a variable in your loop, defined as an integer. Then print the value on each iteration. If you sit there long enough all you will ever see, is an ever growing finite number.

No matter how far ahead in time that you check the loop counter. You must only observe a finite integer value, nothing more or less. I would not call the loop an 'infinite loop', as the iterations of that loop. Are designated as integer values, ultimately finite loops.

You are attempting to force a metaphysical concept (infinity) into a landscape of finite numbers.

 

[SelfSim]

Integers are finite numbers.

References including its context please?

You are attempting to force a metaphysical concept (infinity) into a landscape of finite numbers.

No .. your are attempting to force an absolute definition into a formal theory which triggers the infinite regression problem.

This issue was sorted out (and overcome) back in Hilbert's day.

Justified true belief as a source of knowledge is the root cause of your misconception on the concept of the infinite.

 

[klutedavid]

References including its context please?
No .. your are attempting to force an absolute definition into a formal theory which triggers the infinite regression problem.

This issue was sorted out (and overcome) back in Hilbert's day.

Justified true belief as a source of knowledge is the root cause of your misconception on the concept of the infinite.

Georg Cantor initiated his theory of sets in order to provide a mathematical treatment of infinite sets. Thus the distinction between the finite and the infinite lies at the core of set theory. Certain foundationalists, the strict finitists, reject the existence of infinite sets and thus recommend a mathematics based solely on finite sets. (wikipedia)

But on the other hand to suppose that the infinite does not exist in any way leads obviously to many impossible consequences: there will be a beginning and end of time, a magnitude will not be divisible into magnitudes, number will not be infinite. If, then, in view of the above considerations, neither alternative seems possible, an arbiter must be called in. (Aristotle, Physics, Book 3, Chapter 6)

Mathematics is not metaphysics.

The issue was never sorted out back in Hilbert's day. The herd just moved on.

 

[Ponderous Curmudgeon]

There will always be a finite number of integers, since integers are finite numbers by definition.

At first glance this seems rational but it is your error. Infinity is not a number like other numbers it is the symbol/word we use for endless things.

There is no last finite integer on a number line, there will always be another greater finite integer.

This is true, Infinity is the concept that we use to describe this largest integer. Again, it itself is not an integer, it is a descriptor of this largest number that you cannot put an integer value on because you could always add one more.

If your number line is a finite number line, then all values along that number line must be finite.

Yes a line of finite length is finite, but how many points are on that line? You can keep on dividing the line in half forever and you will never have a piece of that line that has 0 length. (as the line segments get smaller and smaller we can say that they are infinitesimally small) How many fractions are in the series (1/2, 1/4, 1/8, 1/16.... meaning this pattern repeats endlessly. The fractions are all real numbers, but the answer to how many fractions are in the series is infinity.

The finite never can become the infinite as that is illogical.

And nobody said it did.
Try reading this and maybe it will help with your confusion, it is not necessarily an easy concept in that one of my kids got it and the other one didn't. What is Infinity?

 

[sjastro]

Not my logic. Integers are finite numbers.

I would advise you to place a variable in your loop, defined as an integer. Then print the value on each iteration. If you sit there long enough all you will ever see, is an ever growing finite number.

You are stuck in an endless loop of inane comments.
For the umpteenth time it doesn't matter that real numbers and integers are finite numbers; you are not examining numbers as individual entities but in sets which can be finite or infinite.

No matter how far ahead in time that you check the loop counter. You must only observe a finite integer value, nothing more or less. I would not call the loop an 'infinite loop', as the iterations of that loop. Are designated as integer values, ultimately finite loops.

What a load a rubbish.
Its called an infinite or endless loop for a reason when the loop counter doesn't stop and the program runs indefinitely which occurs when it attempts to count an infinite set.
So it's not only the mathematicians and physicists that have got it wrong but also the computer scientists.
This is classic Dunning Kruger stuff.

 

[Ponderous Curmudgeon]

Georg Cantor initiated his theory of sets in order to provide a mathematical treatment of infinite sets. Thus the distinction between the finite and the infinite lies at the core of set theory. Certain foundationalists, the strict finitists, reject the existence of infinite sets and thus recommend a mathematics based solely on finite sets. (wikipedia)

But on the other hand to suppose that the infinite does not exist in any way leads obviously to many impossible consequences: there will be a beginning and end of time, a magnitude will not be divisible into magnitudes, number will not be infinite. If, then, in view of the above considerations, neither alternative seems possible, an arbiter must be called in. (Aristotle, Physics, Book 3, Chapter 6)

Mathematics is not metaphysics.

The issue was never sorted out back in Hilbert's day. The herd just moved on.

Is there a point to this or are you just googling to find snippets that seem to agree with you. The problem is that even if you are a finitist, your logic as presented is flawed and shows lack of understanding.