"Screenshot Recursion via vlc" by vlc team, ubuntu,

Hidro (talk) - Own work. Licensed under GPL via Commons - https://commons.wikimedia.org/wiki/File:Screenshot_Recursion_via_vlc.png#/media/File:Screenshot_Recursion_via_vlc.png

Infinity

A number of objections to the reasoning provided here revolve around the inclusion of infinity ($$\infty$$) in the discussions. Infinity is of course, not a number in the normal sense. It exists only as a result of some sort of limiting process. For example in the Schwarzschild metric, for a distant observer, time of a traveller approaching the event horizon slows down and stops at the event horizon as the metric function becomes infinite. In reality, this can never be observed, as we have to wait an infinite time for it to happen. Whenever we say the metric function becomes infinite we really mean that in the limit of infinite time it will become infinite. For now, it is just a very large number and when we look later, it will be an even larger number.

Notice also that there is a close association between infinity and zero. The reality is that zero cannot be achieved as a measured value either. We normally put this down to quantum mechanics - we cannot have zero momentum or energy, or temperature. We can draw graphs of measurements passing through zero and argue that at one point, the value must be zero. This may be true, but the fact is we will never be able to measure zero due to having available only finite precision.

In physics we have the case of the conductivity of superconductors becoming infinite. Of course, we will never have enough time to check the validity of this statement. This example does show that infinities for all practical purposes, do occur in physics.