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.

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.