Which Infinity do you prefer?, The big one, or the even bigger one. Options

[rhymer]

See the construct here...

http://www.sciam.com/article.cfm?chanID=sa...EAAFAF2776CEFC5

[Rick]

I prefer the smaller countable one. It's big enough for me.

[trojan_libido]

Infinities larger than other infinities? I understand the logic they've used, but come on, we're simply updating our view and our language. The infinite is endless, trying to divide it up and pair it off with another line of infinite thought is crazy.

Its similar to the Universe/Multiverse idea. We've defined the universe as everything, then decided its not. Silly, we should simply divide the universe, not expand it.

[Hey Hey]

Silly, we should simply divide the universe, not expand it.

If you were Lindsay, you'd give it another name!

[Rick]

To unlimitedness, and beyond!

[khenwood]

Can we make up our own infinities?

I would like to introduce the K Henwood infinity!
Granted it's much smaller in scale than the standard infinity, but interesting nonetheless!

[Rick]

I hereby define the KH infinity (KHi) to be equal to 10 to the 50th power (10^50). We can define division by zero to be equal to KHi.

10^50 is larger than any number that has practical application in science or engineering, and division by that (10^-50) is so small as to be zero for all practical purposes.

[Hey Hey]

... so small as to be zero for all practical purposes.

Includes the planet Earth and humans. But one beat of the wings of a butterfly ...

[Rick]

Butterfly effects are not computable, so no need to consider them.

[Hey Hey]

Butterfly effects are not computable, so no need to consider them.

Neither is the weather - just look at the forecasts over 2 days in advance - but a lot of computing power is spent on that! I think weather forecasters must obtain their training and qualifications from the same source as astrologers. In this case PhD means Potluck has Dominated!

[khenwood]

I hereby define the KH infinity (KHi) to be equal to 10 to the 50th power (10^50). We can define division by zero to be equal to KHi.

10^50 is larger than any number that has practical application in science or engineering, and division by that (10^-50) is so small as to be zero for all practical purposes.

Yes! My infinity now has definition!
We had to start somewhere, now didn't we?

[thefield]

theyre just talking about cardinality of numbers. integers and real numbers have different classes of infinity.

basically there are an infinite amount of numbers between 0 and 1, so there must be a "larger" infinity for real numbers over the integers, who do not have any fractions

[Rick]

Actually, the infinity of rational numbers is the same order as the integers: they are both countably infinite. It's the irrationals that get you into the uncountably infinite regime.

[Hey Hey]

Adding infinity to infinity is bigger than infinity? (Hee Hee, Hey Hey!)

[Rick]

Infinity is not a number and is therefore not subject to numerical operations like addition. So adding infinity to infinity is nonsensical.

[Zizius]

Infinity is not a number and is therefore not subject to numerical operations like addition. So adding infinity to infinity is nonsensical.

(lol)True story Rick. I don't know much math wise, but my interest has grown recently...Well, there's my 2 cents for now.

[YinYang]

Interesting debate!
Well, I personally think that infinity Is not a number too,it's more similar to an equation,like this:
1+X=Y
This is the way to represent infinity that we usually use: we start from one, then we add one and we have two, after we add two and we have three, etc etc.
But every equation,in the end, is a representation of infinity, because if we have two or more unknown quantities,the solutino is the infinity.
But this isn't all. We can also suspect that infinity does't exist, because math is a product of human mind, and human mind is limited, in our minds we can have some numbers, but not all the possible numbers. What we can suspect is that the solution of an equation is not the infinity, but the indeterminate and unlimited.
We can imagine one person that starts to count from one for all this life, and before he dies he says to someone to continue counting for all this life from the ultimate number of the first man. The second man does the same, and the counting will be unlimited in the time. But human mind will never catch the number "infinity", so infinity doesn't exist, we only have unlimited numbers, not an infinity.

[Rick]

You can stay on safer ground mathematically if you say "unbounded" in place of "infinity." For example, I can keep typing in this text entry box for as long as I want. It's unbounded. But I can't type forever, so I can never have an infinite amount of text here. It's just unbounded, not infinite.

[Hey Hey]

Infinity is not a number and is therefore not subject to numerical operations like addition. So adding infinity to infinity is nonsensical.

Here's me thinking you brought numbers into the discussion:

I hereby define the KH infinity (KHi) to be equal to 10 to the 50th power (10^50). We can define division by zero to be equal to KHi.

10^50 is larger than any number that has practical application in science or engineering, and division by that (10^-50) is so small as to be zero for all practical purposes.

[Hey Hey]

Surely it all depends on the 'factor' we consider, whether numbers, distance, time, etc, and whether these 'factors' are actually meaningful or 'real' outside the human construct in which they play a part. So, I reckon that infinity is more to do with reality and as such is unlikely to be defined or understood anytime soon, if ever, ever being a human construct of course.

[Rick]

As long as computers crash (and minds boggle) when attempting to divide by zero, we will have this discussion.

[Hey Hey]

As long as computers crash (and minds boggle) when attempting to divide by zero, we will have this discussion.

Then we could end the discussion now ... buy a Mac!

[Rick]

I hate to break it to you, but even Macs will crash if they try to divide by zero!

[Hey Hey]

I hate to break it to you, but even Macs will crash if they try to divide by zero!

That's why they have error catching programming, n'est pa? And the Mac OS is better written, based on UNIX, but with an enhanced usability front end.

[Rick]

Implementation of error trapping and other defensive programming techniques depends on the programmer's competence, not the computer.

[Hey Hey]

Implementation of error trapping and other defensive programming techniques depends on the programmer's competence, not the computer.

Fair enough. Though computers are often involved in sophisticated programming - but that is a different point.

[correlli]

When the universe dies, so does infinity.

[Joesus]

When the universe dies, so does infinity.

But that really doesn't ever happen.

[correlli]

When the universe dies, so does infinity.

But that really doesn't ever happen.

OK, when I die, infinity will cease to exist. You can't really walk up to me after I've died, and convince me that the counter is still ticking over.

[Hey Hey]

When the universe dies, so does infinity.

But that really doesn't ever happen.

OK, when I die, infinity will cease to exist. You can't really walk up to me after I've died, and convince me that the counter is still ticking over.

As when you are asleep or under anesthetic. But then you wake up and we can again. So what was your point?