find a good quote for Strevens adding another layer to the definition for ideali...

[github-actions]

https://github.com/ThomasFKJorna/thesis-writing/blob/1d1627dfe3198ec97f8bdeab0339860d2126f73f/Chapters/II. Idealizations.md#L128

Norton furthermore distinguishes between _well-behaved_ and _ill-behaved idealizations_.[^well-behaved] _Ill-behaved_ idealizations are infinite idealizations whose limit system (the system with the parameter set to zero or infinity) does not match with target system in some way. This mismatch can take two forms [@Norton2012, (3.2, 3.3)]: the limit system might not exist, e.g., an infinite sphere, or the limit system might have a property which conflicts with a property of the target system. For the former, if we define a sphere as all points which are equidistant from some other point, then an infinite sphere does not exist, as there are no points at infinity. ($\mathbb{R}=(-\infty, \infty)$ not $[-\infty,\infty]$) For the latter, Norton imagines modeling an arbitrarily long ellipsoid as an infinite cylinder. While they look similar, the ratio of surface to volume for an ellipsoid is different from that for a cylinder, so the idealization has a fundamental mismatch.


{/**
	* TODO: Create figure which shows the differences between ellipsoid and cylinder volumes
	* labels: visualization
*/}


In short: for Norton infinite idealization simply is the end result of the process of a limiting operation. Furthermore, these idealizations can sometimes be well-behaved, and sometimes ill-behaved.

### Strevens

@Strevens2019a defines infinite idealization (or “asymptotic idealizations” as he calls them, we will stick with infinite here) slightly differently than Norton. Luckily, Strevens does provide a clear definition, which is in contrast to what he calls a “simple” idealization, which "is achieved by the straightforward operation of setting some parameter or parameters in the model to non-actual values, often zero". A clear example is the air-resistance coefficient above. At first, he contrasts this straightforwardly with infinite idealizations in the Nortonian sense, as “in \[infinite\] idealization, by contrast, a fiction is introduced by taking some sort of limit”. We will take this definition to be identical to Norton's.

However, later on in the paper Strevens adds another layer to the definition, 
{/*TODO: find a good quote for Strevens adding another layer to the definition for idealizations*/}
 namely that scientists use infinite idealizations when it is not possible to use a simple idealization to directly set the relevant property to zero (or infinity) 
{/*TODO: Clarify the distinction between infinite and "normal" idealizations for Strevens*/}
. Furthermore, he adds, “\[Infinite\] idealization is an interesting proposition, then, only in those cases where a simple substitution cannot be performed, which is to say only in those cases where a veridical model for mathematical reasons falls apart or otherwise behaves badly at the limiting value.” While Strevens later argues why these interesting cases (Norton's mismatches) _do_ make sense, we do not have to concern us with evaluating their correctness just yet, we simply need to note that Strevens makes the same distinction as Norton here. 

Then, we can define