The both expressions express that the distance between the two numbers $f(x)$ and $L$ should be smaller than $\epsilon$. What is the problem if we rephrase the definition in this way?
2026-04-04 14:18:49.1775312329
Why the definition of a limit of a function can't contain $\left | L-f(x) \right | < \epsilon$ instead of $\left | f(x)-L\right | < \epsilon$?
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It can, there is no problem of writing it the other way, I think its more of a custom.