Although it is often reported because of its common usage, the course generally does not accept the construction "to not X." The infinitive here is "to see," it is not "to NOT see." The correct formulation is "trying not to see," as shown above. The "to not X" alternative may someday be considered for addition, but for now it is not accepted.
It's a pretty old-fashioned rule about not splitting the infinitive - influenced by translation from Latin where, of course, as in Czech, the infinitive can't be split. But splitting it is pretty common usage in modern spoken English... with the infamous "to boldly go" from the Star Trek voiceover introduction as a groundbreaking example from the 1960s. It's been pretty much free rein since then! But okay, I'll stick with the grammatically strict version here for now, thanks.
It did not occur to me the difference should be only in the split/non-split infinitive. It sounds very strange to me, because I learned mainly British English and there the preference for "not to" appears to be stronger. Anyway, this issue should really be resolved among the native English speakers.
The problem with that approach to this issue is two-fold.
1.English doesn't have a singular prescriptive grammar authority.
- You're impeding people's ability to learn the L2 language by focusing on correcting the grammar of their L1 translation. In this case it's not a mis-translation.
I agree with the alternative answer as well. I would also consider, "i'm not trying to see them."
I would actually argue that saying "i'm trying not" translated to Czech would be "nesnazim se." Mainly because the stress-timed part, "i'm trying not", is mostly stressed as a whole component, and 'to see them' is mostly unstressed. However, "i'm trying to not see" stresses different parts: trying; not; and see.
Also, splitting the infinitive with the negative can reduce ambiguity in English. Even in this simple sentence in English, one could ask, are you not trying to see (not trying) or are you trying not to see (not seeing). It is unclear.
To me, it isn't really that important, so this isn't an argument or anything like that. Just a comment. I only said nesnazim se because 'not' is between the verb and the infinitive, making it somewhat ambiguous as to which it is modifying. But as far as duolingo, i'll just continue to use the not between the verb and infinitive, like this example.
Native Hiberno-English speaker here. Both split & non-split infinitive can be correct here but it really depends on context. The split infinitve 'to not see' can put more emphasis on the action, and generally indicates a stronger feeling/intent. However as a general statement it sounds quite natural also to me for my linguistic context, so I would accept both.
It is good to bear in mind that the prevalence of this construction could be different in other native-English-speaking lands.