PM 2Ring wrote:
I think Xanthir has adequately explained what I was getting at. Of course, 10^34 is much larger than 10^24, but 10^24 is just so large already that it's hard to truly appreciate the effect of another "mere" 10 orders of magnitude.
Here's another way of looking at it. Let's say you're a Strong Safety in an American football team, so you play in the defensive backfield.
Now, your opponent is on offense in the 1st quarter, and they have the ball on their own 10 yard line. Do you re-structure your defense based on the location of your goal line? No. Most passing routes only go out 20 yards max.
They pick up 10 yards. Now they're on their 20. Again, your defensive scheme doesn't change, because your goal line is still really far away.
The strategy for the defensive backfield doesn't really change until the offense is under your 40 or 35 yard line. Why? Because at any point farther than that, the goal line is so far away that your immediate concern is plugging up the receivers some 15-20 yards from the line of scrimmage. Or, in other words, regardless of whether the goal line is 99, 90, or 80 yards away, it doesn't change your strategy in the defensive backfield. At that point, it may as well be infinitely far away.
A more mathematical example is boundary layer flow over a flat plate. Basically, the flow profile looks kind of like the right side of the letter U. At the flat plate, the no-slip condition applies, and the velocity is 0. As you get farther above the plate, the velocity increases, but it only increases as high as the free-stream velocity.
Formally, if you construct this system non-dimensionally (so instead of height in centimeters or whatever, we just normalize it to "units"), then the boundary layer flow only approaches free-stream flow in the limit to infinity.
Practically, however, we know this not to be the case, and we observe a point when the boundary layer flow is equal to the free stream flow within, say, 99.5%. The difference in velocity at that point can be considered to be negligible (we couldn't even measure it if we tried).
As it turns out, you don't need to go out to infinity for this case. All you need to do is go about 5 units above the flat plate to observe a 99.999999% match with free-stream. So, in that case, infinity and 5 are effectively indistinguishable.