TITLE: Situations where "Without Loss of Generality" expressions can be used.
QUESTION [6 upvotes]: I am trying to understand in what situations mathematicians use the expression "without loss of generality". The Wikipedia article states that the expression is useful in symmetric situations such as if we assume two outcomes $a$ or $b$, then we can assign a symbolic math where we can make assumptions such as assume $a>b$, so in such scenario we don't loose any generality as we can equally say assume $b>a$, because symbols are symmetric and can be used interchangeably. Is this the correct understanding of the expression?

REPLY [2 votes]: In addition to other answers, WLOG might be used to shorten proof or also to work with concrete notations and objetcs, instead of arbitrary ones.
For example, working in the space of continuous functions over $[a,b]$, $a,b \in \mathbb{R}$, is the same as working over the space of continuous functions over $[0,1]$, since we are able to from one to the other by the affine transformation $f(t) = a+(b-a)t$. Thus, every problem lying in the first, general space for any real bounds $a,b$, can be considered WLOG in the second one, which is fixed and easier to represent.