Infinity in Math and Eternity?

[public hermit]

Indulgence in illogical thinking .. How that comes about from 'mathematical/geometrical thought experiments', is clear evidence pointing to a grossly inconsistent process.

You're familiar with Cusa's writing?

 

[FrumiousBandersnatch]

Infinity is actually treated as a number in maths. But the argument doesn't apply to +infinity because when you have a starting point you can indeed keep counting endlessly. -infinity is a very different issue, because while +infinity starts with real numbers (and therefore includes them), -infinity does not. -infinity starts with infinity and you never reach any real number.

Infinity isn't a number, and -infinity starts with zero, just like +infinity.

As far as time is concerned, you can put your zero point wherever you like.

 

[NxNW]

In math, some infinite numbers are larger than other infinite numbers. They don't work the way you might think they work. Bear in mind that infinite doesn't mean exhaustive. The set of all positive integers {0,1,2,3...} is infinite, but it doesn't contain -1, for example. When you add in the set of negative integers, you might think you now have a larger set with the two sets combined, but in fact they are "equally infinite".

 

[partinobodycular]

An infinite past (in time) is impossible, so there is a difference between "eternity" and "infinity" in this regard.

Oddly enough Aquinas didn't believe that this was true. According to Aquinas a "per accidens" causal series (which is what a temporal series is) may indeed be infinite. Aquinas only argued that a "per se" causal series can't be infinite.

Unfortunately I've never talked to anyone, ever, who could give me an example of a "per se" causal series. Not even Aquinas himself seemed to be able to do that.

 

[durangodawood]

....The set of all positive integers {0,1,2,3...} is infinite, but it doesn't contain -1, for example. When you add in the set of negative integers, you might think you now have a larger set with the two sets combined, but in fact they are "equally infinite".

So an infinite set with more numbers isnt larger?

 

[sjastro]

So an infinite set with more numbers isnt larger?

It is unintuitive but the set of integers {...... -3, -2, -1, 0, 1, 2, 3......} has the same number of elements as the set of natural numbers {0, 1, 2, 3.....}.
This is because each element in the set of integers can be uniquely mapped onto an element in the set natural numbers despite both being infinite sets and the set of integers appearing to have around "twice" as many elements.
The set of integers and natural numbers are examples of a countable set.
The set of real numbers on the other hand which also contains elements such as fractions, irrational numbers etc. is a larger infinite set than natural numbers or integers since there is no unique mapping with the set of natural numbers.
In this case the set of real numbers is known as an uncountable set.

 

[durangodawood]

It is unintuitive but the set of integers {...... -3, -2, -1, 0, 1, 2, 3......} has the same number of elements as the set of natural numbers {0, 1, 2, 3.....}.
This is because each element in the set of integers can be uniquely mapped onto an element in the set natural numbers despite both being infinite sets and the set of integers appearing to have around "twice" as many elements.....

Lets start our unique mapping at 0 and map upwards (which is the only direction we can go given one set doesnt go negative). Once we do that, theres no natural numbers to map onto the negative integers.

And we dont have to match zeros either. We could orient our mapping such that the natural number set 0 aligns with any integer, and there will always be integers heading off into the neg direction with no available natural set map partner - because it used up mapping to integers that head is the pos direction..... right? (thats how it seems to me).

 

[sjastro]

Lets start our unique mapping at 0 and map upwards (which is the only direction we can go given one set doesnt go negative). Once we do that, theres no natural numbers to map onto the negative integers.

And we dont have to match zeros either. We could orient our mapping such that the natural number set 0 aligns with any integer, and there will always be integers heading off into the neg direction with no available natural set map partner - because it used up mapping to integers that head is the pos direction..... right? (thats how it seems to me).

Suppose we start off with two finite sets, say A and B.
A bijection exists if each element in set A can be paired with an element in set B.

Lets now consider two infinite sets, the set of integers Z and the set of natural numbers N.
We can define a bijection f(n) as;

Here n is an element of the set N and f(n) is an element of Z and f(0) = 0.
What we find there is a unique pair (n, f(n)) where elements of each set are paired off despite the fact Z appears to be be a much larger set than N.
The proof of this is found in any pure mathematics textbook on set theory.

When it comes to the set of real numbers R no bijection with N exists.
Hence R is an uncountable infinite set as it contains an infinite number of elements which cannot be paired off with elements in N.

 

[NxNW]

Lets start our unique mapping at 0 and map upwards (which is the only direction we can go given one set doesnt go negative). Once we do that, theres no natural numbers to map onto the negative integers.

Start at zero and work outward in both directions. For example 0, -1, 1, -2, 2, -3, 3, etc are all assigned 1, 2, 3, 4, 5, 6, 7 respectively, and so on. I'll never run out of positive integers even though I seem to be "using them up" twice as fast as the full set of integers.

 

[Kylie]

Hi everyone,

I got to thinking about the concept of infinity in mathematics and the concept of eternity described in the Bible, I could use some help. I think there is a parallel between infinity in math and eternity, there is something there but it is not coming to me, let me know if you have anything to add. One thing that did come to me- with infinity infinity + any number = infinity. Is there a Godly principal in this? Thanks

In maths, there are different kinds of infinity.

 

[FrumiousBandersnatch]

In maths, there are different kinds of infinity.

An infinite hierarchy of infinities...

 

[Larniavc]

Hi everyone,

I got to thinking about the concept of infinity in mathematics and the concept of eternity described in the Bible, I could use some help. I think there is a parallel between infinity in math and eternity, there is something there but it is not coming to me, let me know if you have anything to add. One thing that did come to me- with infinity infinity + any number = infinity. Is there a Godly principal in this? Thanks

My understanding is that in maths there are several ‘infinities’. So, many gods?

 

[Sophrosyne]

Infinity is definitely not a number but rather a concept. One can consider use the concept to describe other things such as never ending time, and any other thing that continues onwards. Our limits to understanding infinity is because we are essentially not infinite in but one way and that way is our soul that based upon the Bible is not ending but continues on after death and the Bible equates that God is the source of our soul and God is the (essentially) author of the infinite.

We try and fumble around to understand the concept of infinity based upon what we see as finite and expanding that finiteness till it reaches such hugeness that we start to lose our grasp upon what to compare it to. It is like 3 persons, one growing up in a town of 1000 people, another in a city of 100 thousand and a third a city of 10 million. The person from the smallest of these may consider a city of 10 million as overwhelming in scope approaching in their observation.... infinity while someone from 100 thousand city may be able to fathom it, it may take a lot of effort to do so. If we thus take all three and consider 1 trillion people we may find that even the person from a city of 10 million will be similarly dwarfed in their being able to conceptualize it. Now we could go on to consider 1 quadrillion or quintillion or whatever but after a certain point we have to consider the numbers more than being able to visualize such massive amounts.

I think that being in a finite universe (as we can conceptual it) the idea of infinity doesn't fit, but in God's domain with his powers not hampered by the dimensions and laws of our universe it may be possible to conceptualize infinity after all. One could equate learning and growing in knowledge forever and without time (perhaps one could consider time= infinite and unmeasurable in that thinking) then things that are impossible could become totally possible.... and in becoming possible without the passage of time (in our universe) is mind boggling especially if someone could operate in another universe that favors laws that can make the most use of the infinite.

The closest I have come to fathoming infinity I think is when I was 100% healthy and feeling good and had no thought of ever changing, growing old and dying. In my mind even though time was passing I was oblivious to it and in that I thought I could last forever. It is when I got older that I did find my body changing and health not quite as robust that I then shifted that thinking/feeling towards living forever with God. We will all have a better concept of infinity in heaven? I absolutely think so.

 

[Astrophile]

Eternity can mean "without beginning and without end", while applying the term infinity to time can only mean "with a beginning but without end". An infinite past (in time) is impossible, so there is a difference between "eternity" and "infinity" in this regard.

A universe with a beginning but no end would be semi-infinite in time, whereas one with neither a beginning nor an end would be infinite.