A direct application would need that you have an uncountable variable. You might want to do this if you have enough evidence to say this confidently. As a simple example imagine a real-valued graph where all your data points lie almost on the identity diagonal. You might then want to infer a variable which is the identity.
As a more general application, we want to model infinities because the world is probably infinite in some aspects. We then want a theorem that tells us, that even if the underlying model is infinite, if you have enough data points then you are close enough, like with the Strong law of Large numbers, for example.
A direct application would need that you have an uncountable variable. You might want to do this if you have enough evidence to say this confidently. As a simple example imagine a real-valued graph where all your data points lie almost on the identity diagonal. You might then want to infer a variable which is the identity.
As a more general application, we want to model infinities because the world is probably infinite in some aspects. We then want a theorem that tells us, that even if the underlying model is infinite, if you have enough data points then you are close enough, like with the Strong law of Large numbers, for example.