Maths texts and lectures often refer to observations as being "easy to check", "trivial" or "obvious." It would seem to me that such phrases (at least sometimes) risk the consequence that students will find difficulty in checking such "easy" results, have their confidence thereby undermined and thereby have their mathematical education impaired. I'm asking in this post whether this is a concern. Perhaps the answer is different depending on the level of the students, and my guess is that this concern is more valid for undergraduates. (I would doubt that it would bother a well-known elite mathematician if he or she struggled to verify a fact that the seminar speaker insisted was "obvious.")
I see many possible answers to my (implicit) question, and wonder what view respondents take. 1) "Easy" and "obvious" etc are simply useful synonyms to mean that such facts can be applied simply by thinking through the consequences of definitions, and that no extra research is needed or applying unexpected theorems. Students know this so there is no problem with such words. 2) As above regarding the meaning of terms like "easy" etc. However, students aren't adequately explained that that is what mathematicians mean, and thus may feel insulted as a result of not understanding what is meant by "easy", "obvious", etc. . 3) Rather than using such words and explaining their meanings, it's best to just avoid words like "obvious" etc. to avoid such misunderstandings. 4) Facts that are said to be "easy" or "obvious" should indeed require not much effort from the student besides a little thought. If students are disconcerted because they don't find such things obvious, then they are reading a too-advanced text or studying the wrong subject.