Phrases I don’t like that are often used in text books

I am sure that people who read technical books related to mathematics have come across the following phrases at least once.

• “It is easy to show that … “
• “The derivation of … is left as an exercise.”
• “The blah blah problem therefore amounts to ….(some long formula) …”
• “Clearly, blah blah of this is blah blah of that …”

There is nothing wrong about the mentioned phrases. The problem is that these phrases are often used without any justification or clear explanation. Around 80% of the time I found “It is easy to show that…”, it is NOT easy for me.  Around 90% of the time I found “The derivation of … is left as an exercise.”, I cannot derive the thing I want. Almost every time I found “The blah blah problem therefore amounts to ….(some long formula) …”, I do not know why the given formula is related to the original problem. Finally, every time I found “Clearly, ….”, it is NOT that obvious for me to figure out. It takes some time.

This post is just a complaint from a stupid man like me. Just think about it. If you can easily derive a long formula, what is the point of reading the book ? You are already able to do it by your own. This implies that many students read the book because they do not know how to derive those. They want to know it. That is why they read the book! In the end, I still wonder why the book is often written in that way. Is it so troublesome to add more details .. ?