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Your stumbling from pillar to post.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.
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.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.
An infinite series of anything is undefined.I know understand why;
or why the sum of this infinite series converges;
I understand why the set of real numbers R is anuncountable infinite setwhile the set of integers Z is acountable infinite set.
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?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 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.
That is not all that is holding you back.A more detailed account of this subject can be found in this link.
What a load of nonsense.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.
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?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?
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?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?
An axiom may be to blame for this contradiction.
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.
Boolean algebra - the Law of Identity for classes: 'Every class includes itself'.You seem to be thinking that the infinite can be contained within a set? An axiom may be to blame for this contradiction.sjastro said: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
Your making a simple mistake.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 trying to increase the complexity with set theory.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.
You, yourself, are discussing classes (or sets) of number types.Your trying to increase the complexity with set theory.
They made a mistake and they cannot see their error.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.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.
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.Not a fixation at all. That is the definition of real numbers. They are finite numbers regardless of the tapestry you weave.
.. and you always will, as long as you choose not to research your topic and learn from that research.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.
You misunderstand the definition of a finite number.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.
Your seeing a trend in those real numbers?.. 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... and you always will, as long as you choose not to research your topic and learn from that research.
We are discussing infinite universes .. get on topic!You misunderstand the definition of a finite number.
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.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.
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.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.
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