What are the implications of an infinite large universe?

[klutedavid]

You clearly do not understand what a real number is.
The closed interval [0,1] is bounded and contains an infinite number of real numbers.
Here is a hint there is no paradox since real numbers can be expressed to an unlimited number of decimal places.

Your stumbling from pillar to post.

Your closed interval is BOUNDED but if something is infinite it is not bounded.

An 'infinite number of real numbers' is a paradox. Real numbers are finite numbers, finite numbers are by definition not infinite.

 

[klutedavid]

Not this again.
I’m always intrigued how a stranger can pontificate what I or anyone else does not understand about infinity.

I understand the calculation of an area under the curve y = f(x) using integral calculus is the limit of summing an infinite number of infinitesimally small rectangles.

You cannot sum an infinite number of rectangles. Your applying mathematical operands that apply to finite numbers only. There is no such thing as an infinite number, a paradox again. Limits in Calculus are exactly that; limitations on a function for example.

I know understand why;

or why the sum of this infinite series converges;

An infinite series of anything is undefined.

I understand why the set of real numbers R is an​

uncountable infinite set​

while the set of integers Z is a​

countable infinite set​

.​

You seem to be thinking that the infinite can be contained within a set?

An axiom may be to blame for this contradiction.​

More appropriate to this thread is measuring the curvature of spacetime using the CMB. If the curvature is zero or flat then the evidence is very strong the universe is infinitely large.

The human mind cannot understand infinity, we cannot adequately even define it. Your doing it again, 'the universe is infinitely large'. You seem to have a definition of infinity that I do not know. How can an entity be infinitely large?

The only thing holding us back in declaring the universe is infinitely large is the question of inflation which was an exponential increase in the rate of expansion in the very early history of the universe.

A more detailed account of this subject can be found in this link.

That is not all that is holding you back.

An accurate value for the Hubble constant is a problem.

Dark Energy and Dark Matter represents a major problem.

Attempting to reconcile Quantum Theory with General Relativity is another problem.

The Big Bang itself may also be in some trouble.

 

[SelfSim]

This latest load of codswallop reminds me of 'Mr NoBlackHoles', Stephen Crother's self-entitled 'disproof' of the existence of black holes .. (which was all based on the 'mental block' misconception .. which was really caused by a falling out with academia).

The other way to relate to it, is via the notorious loony: Miles Mathis and his recalculated value of pi.

.. Not interested ..

 

[sjastro]

Your stumbling from pillar to post.

Your closed interval is BOUNDED but if something is infinite it is not bounded.

An 'infinite number of real numbers' is a paradox. Real numbers are finite numbers, finite numbers are by definition not infinite.

What a load of nonsense.
[0,1] is clearly a bounded infinite set for real numbers.
It's bounded because there are no elements less than 0 or greater than 1.
If you count all the numbers in the set to one decimal place there is a finite number, as there is for two, three, four decimal places and so on.
Notice a trend here?
There is no limit to the number of decimal places that defines a real number hence the set is an infinite set.

On the other hand [0,1] is a finite set for integers as there are only two elements in the set, 0 and 1.

 

[renniks]

If God is eternal then He exists outside of time. If He is infinite, He exists within time. Lets go Option 2.

If He has existed for an infinite amount of time then time itself has, obviously, existed for an infinite amount of time.
Time measures change. It's the definition of time. If nothing existed then time would not exist.
So something has been changing for an infinite amount of time.
So something has always existed.

I'm quite happy with that. But are you?

No. God is both eternal and infinite. To claim matter is infinite is to take it outside of the realm of science. We can't fully comprehend timelessness. But why would time exist at all for an eternal being?

 

[sjastro]

You cannot sum an infinite number of rectangles. Your applying mathematical operands that apply to finite numbers only. There is no such thing as an infinite number, a paradox again. Limits in Calculus are exactly that; limitations on a function for example.An infinite series of anything is undefined.

You seem to be thinking that the infinite can be contained within a set?

An axiom may be to blame for this contradiction.​

The human mind cannot understand infinity, we cannot adequately even define it. Your doing it again, 'the universe is infinitely large'. You seem to have a definition of infinity that I do not know. How can an entity be infinitely large?

​

That is not all that is holding you back.

Did you try reading my post?
The point was to give to you a few examples where infinity which you summarily placed in the "fiction category" is explicitly used in calculations and in theory.
Yes infinity is a difficult concept to grasp, however some have a greater understanding than others and your level of understanding is demonstrably limited by the argument of repetition fallacy.

An accurate value for the Hubble constant is a problem.

Dark Energy and Dark Matter represents a major problem.

Attempting to reconcile Quantum Theory with General Relativity is another problem.

The Big Bang itself may also be in some trouble.

This is an example of your limited comprehension.
Did the link I provided mention anything about Hubble's constant, dark energy or dark matter?
These are parameters which pertain to the observable universe which is finite.
The article was about the entire universe which is what lies beyond the particle horizon of the observable universe.

 

[SelfSim]

I understand why the set of real numbers R is an uncountable infinite set while the set of integers Z is a countable infinite set

You seem to be thinking that the infinite can be contained within a set? An axiom may be to blame for this contradiction.

Boolean algebra - the Law of Identity for classes: 'Every class includes itself'.

Set theory then starts out with a fundamental binary relation between an object and a set.

Since sets are objects, the membership relation can relate to the sets as well.

 

[klutedavid]

What a load of nonsense.
[0,1] is clearly a bounded infinite set for real numbers.
It's bounded because there are no elements less than 0 or greater than 1.
If you count all the numbers in the set to one decimal place there is a finite number, as there is for two, three, four decimal places and so on.
Notice a trend here?
There is no limit to the number of decimal places that defines a real number hence the set is an infinite set.

On the other hand [0,1] is a finite set for integers as there are only two elements in the set, 0 and 1.

Your making a simple mistake.

Real numbers are finite numbers.

Finite numbers are not infinite.

Whether you have one or more decimal places, the real number is still finite.

No matter how many places you tend towards with a real number. The fact remains, you will only tend towards finite numbers.

There will always be a larger real number after every real number, in any direction you take it. No matter how far you travel on the track, guess what? There is always a larger real number.

Your seeing a trend that does not exist in the world of finite numbers.

 

[klutedavid]

Boolean algebra - the Law of Identity for classes: 'Every class includes itself'.

Set theory then starts out with a fundamental binary relation between an object and a set.

Since sets are objects, the membership relation can relate to the sets as well.

Your trying to increase the complexity with set theory.

 

[SelfSim]

Your trying to increase the complexity with set theory.

You, yourself, are discussing classes (or sets) of number types.

You are also fixated on just one law of logical thought.
One has to consider all of them simultaneously, all of which, was already sorted out in the last century by the great mathematician philosophers.
You need to get yourself up to date.

 

[klutedavid]

You, yourself, are discussing classes (or sets) of number types.

You are also fixated on just one law of logical thought.
One has to consider all of them simultaneously, all of which, was already sorted out in the last century by the great mathematician philosophers.
You need to get yourself up to date.

They made a mistake and they cannot see their error.

Real numbers are always real numbers, always finite numbers.

0.1
0.2
0.003

See a trend towards infinity?

I see no trend, they a merely finite numbers.

 

[klutedavid]

You, yourself, are discussing classes (or sets) of number types.

You are also fixated on just one law of logical thought.
One has to consider all of them simultaneously, all of which, was already sorted out in the last century by the great mathematician philosophers.
You need to get yourself up to date.

Not a fixation at all. That is the definition of real numbers. They are finite numbers regardless of the tapestry you weave.

 

[SelfSim]

Not a fixation at all. That is the definition of real numbers. They are finite numbers regardless of the tapestry you weave.

Judging from the speed of your response (and its content), you have failed in going to check up, and learn about, the history of evolution in propositional (calculus) logic.

You thus appear to wish to perpetuate your ignorance of what your argument relies upon.

 

[SelfSim]

Real numbers are always real numbers, always finite numbers.
0.1
0.2
0.003

See a trend towards infinity?

I see no trend, they a merely finite numbers.

.. and you always will, as long as you choose not to research your topic and learn from that research.

 

[klutedavid]

Judging from the speed of your response (and its content), you have failed in going to check up, and learn about, the history of evolution in propositional (calculus) logic.

You thus appear to wish to perpetuate your ignorance of what your argument relies upon.

You misunderstand the definition of a finite number.

 

[klutedavid]

.. and you always will, as long as you choose not to research your topic and learn from that research.

Your seeing a trend in those real numbers?

Your thinking, their getting smaller and smaller, tending towards even smaller real numbers. On and on it goes, yet we always arrive at smaller real numbers. Your wrong and you cannot admit it.

 

[klutedavid]

.. and you always will, as long as you choose not to research your topic and learn from that research.

There just real numbers and there is nothing to research. Real numbers are finite and always finite numbers.

 

[SelfSim]

You misunderstand the definition of a finite number.

We are discussing infinite universes .. get on topic!

 

[Ponderous Curmudgeon]

They made a mistake and they cannot see their error.

Real numbers are always real numbers, always finite numbers.

0.1
0.2
0.003

See a trend towards infinity?

I see no trend, they a merely finite numbers.

yeah, the trend is obvious, you can always have another number between any two real numbers, thus the set trends to infinity even though any given number is finite as you describe it. You are confusing the meaning of finite in this case. A real number is a real number. a given real number is finite, but the set of real numbers between 0 and 1 is infinite.

 

[klutedavid]

yeah, the trend is obvious, you can always have another number between any two real numbers, thus the set trends to infinity even though any given number is finite as you describe it. You are confusing the meaning of finite in this case. A real number is a real number. a given real number is finite, but the set of real numbers between 0 and 1 is infinite.

As I said previously, there are no unbounded sets of real numbers. Real numbers are finite numbers. A set of real numbers is always a finite set.

The definition of real numbers excludes a finite set from being an infinite set.

The first bound is zero and the other bound is one. That is a bounded set of real numbers.

The infinite is described as unbounded.