inzicht

You've offered me some clarity on this. I would think that because mathematics are so involved as modelling tools in physics it's no surprise the two are frequently confounded. As my interest in physics is fairly recent I have to research much of this. I can see how a discontinuity in an equation could easily act as a source of 'break down'. Thanks again.

Could you give an example of an equation "giving a wrong answer that is theoretically possible". In that case the equation would have remained true or accurate within its own theoretical model, and hence not broken down, but nonetheless be "wrong" for predictions not valid in reality. In that case the equation most definitely does not break down. Still, it makes for unsatisfying predictions. I will have to look up infinite probabilities. If that is "literal nonsense" but still within an otherwise valid equation could it not just be an issue with our model of understanding which cannot make sense of it?

"The Equation Breaks Down" I remember hearing this statement in a physics documentary some time ago. I presume it to mean that an equation which gives valid or verifiable predictions within a certain range, once that range is exceeded, produces incorrect statements or values (for example Newtonian Physics cannot describe activity on a quantum level, therefore its mathematical predictions would "break down"). That an equation should "break down" on one level but remain true on another would seem to mean that the equation is not in fact true or absolute. I would like to know any other current mathematical examples in Physics where equations appear to collapse or produce seemingly nonsensical predictions. Surely the root of the collapse is in the model which cannot make sense of the equation's data, rather than the equation itself. Is this best solved empirically? Thanks in advance.