Question

[Dr Unne]

[qq=Yams]For practical purposes infinity is infinity no matter which way you look at it.[/qq]

Actually, no. There are different kinds of infinities and the differences matter. They matter in practical ways like for computer programming.

For practical purposes infinity is infinity no matter which way you look at it.

Right, it's like asking if there are more whole numbers (1,2,3,4...) or more even numbers.

There are more whole numbers than even numbers. Both have infinite amount of numbers though.

It doesn't make any sense to say that there are "more" of one than the other, when looking at infinite sets. You could only say that about a finite subset.

[rubah]

This square you're mentioning, if it's the length of an infinite line squared, that's like a space, right?

[nik0tine]

I would guess that the points on the plane are a sort of 'less restricted' infinity. It's still an infinite number, but the plane allows them to be organized differently. I think.

[Yamaneko]

[qq=Yams]For practical purposes infinity is infinity no matter which way you look at it.[/qq]

Actually, no. There are different kinds of infinities and the differences matter. They matter in practical ways like for computer programming.

I'm interested, could you give an example without confusing me too much?

[GhandiOwnsYou]

Have we really reverted back to 2nd grade?

IE: UR STOOPID!
UR STOOPIDER!
UR STOOPID TIMES A THOUSAND!
UR STOPPID TIMES A MILLION!
UR STOOPID TIMS A FINITY!
UR STOOPID TIME A INFINITY + 1!

[Peegee]

[qq=Yams]For practical purposes infinity is infinity no matter which way you look at it.[/qq]

Actually, no. There are different kinds of infinities and the differences matter. They matter in practical ways like for computer programming.

For practical purposes infinity is infinity no matter which way you look at it.

Right, it's like asking if there are more whole numbers (1,2,3,4...) or more even numbers.

There are more whole numbers than even numbers. Both have infinite amount of numbers though.

It doesn't make any sense to say that there are "more" of one than the other, when looking at infinite sets. You could only say that about a finite subset.

It doesn't make any sense, which is why when I learned that there are 'more' points in a square than a line, I was confused to no end.

The metaphors don't apply.

[Dr Unne]

[qq=Yams]For practical purposes infinity is infinity no matter which way you look at it.[/qq]

Actually, no. There are different kinds of infinities and the differences matter. They matter in practical ways like for computer programming.

I'm interested, could you give an example without confusing me too much?

Umm, let's see. There are a lot of algorithms for producing digits of pi. Pi has an infinite number of non-repeating digits (so far as we can tell now). The best we can do is approximate it as best as possible. For example some algorithms are an infinite series whose limit is pi as you take it out to infinity; so the more members of the series you calculate, the closer your result is to pi. But you'd need to do an infinite number of members of the series to get exactly pi.

However not all algorithms are equal. Some approach pi much faster than others. So if you do a day's worth of work, you'd get more digits of pi with one algorithm than the other. It depends how quickly they converge. So even though they are both infinite series, and both have the same limit (so both would give the same answer if you took an infinite number of members of the series), they are practically different in terms of time and productivity.

That may not have anything to do with anything we're talking about though. I may have just made that up.