can you go to Infinity...and beyond?

[beenherebeforeagain]

as the subheading of this article sayd..."my brain hurts."

Infinities can be of different sizes, but maybe that only has to do with math...
Can You Count Past Infinity?

 

[SalixIncendium]

as the subheading of this article sayd..."my brain hurts."

Infinities can be of different sizes, but maybe that only has to do with math...
Can You Count Past Infinity?

I don't think I'd have the time (literally). Even if I ticked off two numbers a second (which gets more difficult as the number grows, I'd still get to just over 44 million even if I dedicated a lifetime to it.

Unless of course I get to seven and cheat by rotating the symbol ninety degrees.

 

[ChristineM]

I have spent quite a lot of time trying to imagine infinity, infinitely large or infinitely small. Funny really, i had a harder time trying to get my head around infinitely small, molecules, atoms, particles... What next???
It was an escape during a particularly bad period of my life.

Never got there though.

 

[beenherebeforeagain]

I don't think I'd have the time (literally). Even if I ticked off two numbers a second (which gets more difficult as the number grows, I'd still get to just over 44 million even if I dedicated a lifetime to it.

Unless of course I get to seven and cheat by rotating the symbol ninety degrees.

I'd have fallen asleep LONG before that...

 

[MonkeyFire]

Infinite time with limited amount of living things and space. The one good thing about infinite space is sending evil people out there into the unihabitated vast to get lost.

 

[beenherebeforeagain]

I have spent quite a lot of time trying to imagine infinity, infinitely large or infinitely small. Funny really, i had a harder time trying to get my head around infinitely small, molecules, atoms, particles... What next???
It was an escape during a particularly bad period of my life.

Never got there though.

I understand (from others who understand it) that infinities are necessary for some things...but for the life of me, when I realized that going further than, say, 3.14159 would simply be wasted effort in almost any actual real-world setting that I would be likely to encounter (that is, the error of measurement would negate the need for precise calculations), I pretty much gave up on higher math...

 

[Twilight Hue]

as the subheading of this article sayd..."my brain hurts."

Infinities can be of different sizes, but maybe that only has to do with math...
Can You Count Past Infinity?

Yep. Infinity plus 1. :Op

 

[beenherebeforeagain]

Yep. Infinity plus 1. :Op

Yeah, but my infinity plus 1 is a least 10^100 times larger than your infinity plus 1...

 

[`mud]

Ahh.....infinity...that invinsibility of no existance !
That point were nothing exists !
What direction is it ?
Where does the Cosmos end ?

 

[Polymath257]

Infinity is one of those things you get better understanding with practice. The problem is that there is more than one type that is typically used.

The easiest type of infinity that arises has to do with limits and approximations. This is the sort that was mentioned above about pi=3.1415926535.... This is actually a way of thinking about successive approximations, 3.1, 3.14, 3.141, 3.1415, 3.14159, ... with each approximation getting closer to the 'goal'. of course, there is nothing special about pi in this. One-third is represented by .3333.... and this is also a sequence of better and better approximations to the goal . There *is* a difference (irrational numbers versus rational numbers), with one repeating cyclically, and the other not. But the 'infinite expansion' part is the same for both.

The next easiest type is cardinality. Here, two sets are the 'same size' if there is a way to pair off members of each with members in the other in a one-to-one way that pairs everything. But, when dealing with this type of infinity, a lot of intuitions that arise in the study of finite sets fail. In particular, it is quite possible for a set and a proper subset to have the 'same size' in this sense.

For example, we can pair every positive integer (1,2,3,4,5,...) with the even positive integers (2,4,6,8,10,...) by just pairing each with its double.

Our intuition is violated because we think of there being 'more' integers than even integers (which is true when dealing with subsets), even though the two have the same cardinality (they can be paired off perfectly). The point is that we have to be precise *which* version of 'larger' we mean in such situations.

Another violation of intuition is that there are infinite sets that are NOT the same size as these: there are legitimately different 'sizes' of infinity.

While this is strange at first, it is something that becomes more natural with familiarity and ALL mathematics students at a certain level are required to be able to deal with this notion of infinite size.

Finally (at least here), there is the notion of ordinality, which has to do with the order of things (first, second, third, etc). The first infinite ordinality is that of the positive natural numbers, 1,2,3,4,5.....
But we can then put another ordinal after all of these (usually called omega) and keep on going, so we have

1,2,3,4,5,...,omega, omega+1, omega+2, ....., omega*2, ..., omega*omega,....

All of these are the 'same size' when viewed in terms of cardinality, though.

In modern math, this also continues to ordinals that are NOT the same size of these in terms of cardinality.

So this is three different notions of 'infinity' that give different answers and are appropriate in different contexts. It is possible to develop intuition on how these all work and how they interact, but at base there is more than one notion of infinity that needs to be addressed and confusing the different notions leads to all sorts of badness.

 

[Terry Sampson]

Where does the Cosmos end ?

Who, of any importance, says it has to end somewhere?

 

[beenherebeforeagain]

Infinity is one of those things you get better understanding with practice. The problem is that there is more than one type that is typically used.

The easiest type of infinity that arises has to do with limits and approximations. This is the sort that was mentioned above about pi=3.1415926535.... This is actually a way of thinking about successive approximations, 3.1, 3.14, 3.141, 3.1415, 3.14159, ... with each approximation getting closer to the 'goal'. of course, there is nothing special about pi in this. One-third is represented by .3333.... and this is also a sequence of better and better approximations to the goal . There *is* a difference (irrational numbers versus rational numbers), with one repeating cyclically, and the other not. But the 'infinite expansion' part is the same for both.

The next easiest type is cardinality. Here, two sets are the 'same size' if there is a way to pair off members of each with members in the other in a one-to-one way that pairs everything. But, when dealing with this type of infinity, a lot of intuitions that arise in the study of finite sets fail. In particular, it is quite possible for a set and a proper subset to have the 'same size' in this sense.

For example, we can pair every positive integer (1,2,3,4,5,...) with the even positive integers (2,4,6,8,10,...) by just pairing each with its double.

Our intuition is violated because we think of there being 'more' integers than even integers (which is true when dealing with subsets), even though the two have the same cardinality (they can be paired off perfectly). The point is that we have to be precise *which* version of 'larger' we mean in such situations.

Another violation of intuition is that there are infinite sets that are NOT the same size as these: there are legitimately different 'sizes' of infinity.

While this is strange at first, it is something that becomes more natural with familiarity and ALL mathematics students at a certain level are required to be able to deal with this notion of infinite size.

Finally (at least here), there is the notion of ordinality, which has to do with the order of things (first, second, third, etc). The first infinite ordinality is that of the positive natural numbers, 1,2,3,4,5.....
But we can then put another ordinal after all of these (usually called omega) and keep on going, so we have

1,2,3,4,5,...,omega, omega+1, omega+2, ....., omega*2, ..., omega*omega,....

All of these are the 'same size' when viewed in terms of cardinality, though.

In modern math, this also continues to ordinals that are NOT the same size of these in terms of cardinality.

So this is three different notions of 'infinity' that give different answers and are appropriate in different contexts. It is possible to develop intuition on how these all work and how they interact, but at base there is more than one notion of infinity that needs to be addressed and confusing the different notions leads to all sorts of badness.

Still, you lost me shortly after the first sentence...

But really, what the heck does Buzz Lightyear MEAN when he says "To Infinity...And Beyond?"

 

[paarsurrey]

as the subheading of this article sayd..."my brain hurts."

Infinities can be of different sizes, but maybe that only has to do with math...
Can You Count Past Infinity?

"math"

Math is only valid in the material and physical realms like Physics, it leads nowhere in ethical, moral and spiritual realms. Right, please?

Regards

 

[paarsurrey]

can you go to Infinity...and beyond?

I say if one could go to somewhere where there is no relativity, one would reach to infinity. Right, please?

Regards

 

[beenherebeforeagain]

"math"

Math is only valid in the material and physical realms like Physics, it leads nowhere in ethical, moral and spiritual realms. Right, please?

can you go to Infinity...and beyond?

I say if one could go to somewhere where there is no relativity, one would reach to infinity. Right, please?

Regards

Could be. Math is good for some things, not so much for others...but there's a good many things that are not just physical that mathematics can describe...the Golden Mean, for example.

As for ethical, moral, spiritual, and I would add aesthetics, maybe we just don't know enough to see how math applies to all that.

And for someplace without relativity? I have a hard enough time comprehending where we do have relativity, and I have no idea whether a place without would be, or would allow one to be or reach, infinity.

For me, infinity just isn't that useful of a concept.

 

[paarsurrey]

Could be. Math is good for some things, not so much for others...but there's a good many things that are not just physical that mathematics can describe...the Golden Mean, for example.

As for ethical, moral, spiritual, and I would add aesthetics, maybe we just don't know enough to see how math applies to all that.

And for someplace without relativity? I have a hard enough time comprehending where we do have relativity, and I have no idea whether a place without would be, or would allow one to be or reach, infinity.

For me, infinity just isn't that useful of a concept.

"Math is good for some things"

There still exist tribal societies who can count only up-to three, beyond that it is many or innumerable with them. Is the innumerable same as infinity, please?
Where there is no time and place, can we describe it the Absolute, please?

Regards
____________
"Researchers discovered the Piraha tribe of Brazil, with a population of 200, have no words beyond one, two and many.
The word for "one" can also mean "a few", while "two" can also be used to refer to "not many".
BBC NEWS | Americas | Brazil tribe prove words count"

"The Mundurukú, another remote tribe, studied by a French team led by Pierre Pica and Stanislas Dehaene, only have words for numbers up to five. Pica and colleagues showed that the Munduruku could compare large sets of dots and add them together approximately. However, when it came to exact subtraction, they were much worse.
Mundurukú participants saw on a computer screen dots dropping into a bucket, with some dots falling through the bottom. They had to calculate exactly how many were left. The answer was always zero, one or two, and they had to select the correct answer. They were quite good, but not perfect, when the initial numbers dots going in and falling out were five or fewer, the limit of their vocabulary, but many of them were doing little better than guessing when the numbers were more than five, even though the answers were always zero, one or two"
What happens when you can't count past four?

 

[beenherebeforeagain]

"Math is good for some things"

There still exist tribal societies who can count only up-to three, beyond that it is many or innumerable with them. Is the innumerable same as infinity, please?
Where there is no time and place, can we describe it the Absolute, please?

Regards

Not sure where you're trying to go with this. I don't think innumerable (whether theirs or ours) is necessarily the same as infinity, and as @Polymath257 explained, there are different kinds of infinity, and conflating them is not good reasoning.

And no, I don't think that there is a "where" where there is no time and place...

Personally, I'm doubtful that there is an Absolute, but if there is, it would have to include all times and places, not be without them. Certainly, I would think any such Absolute would be far beyond my personal and the range of human ability to comprehend.

 

[paarsurrey]

Not sure where you're trying to go with this. I don't think innumerable (whether theirs or ours) is necessarily the same as infinity, and as @Polymath257 explained, there are different kinds of infinity, and conflating them is not good reasoning.

And no, I don't think that there is a "where" where there is no time and place...

Personally, I'm doubtful that there is an Absolute, but if there is, it would have to include all times and places, not be without them. Certainly, I would think any such Absolute would be far beyond my personal and the range of human ability to comprehend.

"infinity"

So, kindly let know as to what one understands from the word "infinity", one's own understanding of it, not from a lexicon nor the mathematical term/concept "infinity", please.

Regards

 

[ChristineM]

I understand (from others who understand it) that infinities are necessary for some things...but for the life of me, when I realized that going further than, say, 3.14159 would simply be wasted effort in almost any actual real-world setting that I would be likely to encounter (that is, the error of measurement would negate the need for precise calculations), I pretty much gave up on higher math...

Higher maths is not for me, all those squiggly characters leave me cold.

One point about infinity, its a mathematical concept not (or rarely) used in science.
"To invoke infinity means something has gone terribly wrong." - Neil Turok, director, perimeter institute for theoretical physics.

 

[Polymath257]

Truthfully, I find it *much* more difficult to 'understand' some really, really larger, *finite* numbers. Graham's number, for example.

To get a handle on this number, we start with the notion that multiplication is repeated addition: so

4*5=4+4+4+4+4 = 20

The next level is exponentiation, which is repeated multiplication:

4^5=4*4*4*4*4 = 1024

Just to let you know, the estimate for the number of fundamental, subatomic particles in the observable universe is around 10^80.

The next stage doesn't really have a name, but it is repeated exponentiation (I use two ^^ to show this).

3^^4 = 3^3^3^3 = 3^3 ^27 = 3^7625597484987 (which is huge).

Again, the next stage is written with three ^^^

3^^^4 = 3^^^3^^^3^^^3^^^3

This process continues for any number of ^.

Next, we do another operation, which I will write &. The second number here tells how many ^^ to use, so

4&2=4^^4

4&5=4^^^^^4.

But now we can repeat this process:

4&&5=4&4&4&4&4

4&&&3=4&&4&&4

Next, we can use another symbol, say $ to say how many & to use:

4$5=4&&&&&4.

Graham's number is then 3$64. This number actually came up in research mathematics!